StudySmarter - The all-in-one study app.

4.8 • +11k Ratings

More than 3 Million Downloads

Free

Triangles

- Calculus
- Absolute Maxima and Minima
- Absolute and Conditional Convergence
- Accumulation Function
- Accumulation Problems
- Algebraic Functions
- Alternating Series
- Antiderivatives
- Application of Derivatives
- Approximating Areas
- Arc Length of a Curve
- Arithmetic Series
- Average Value of a Function
- Calculus of Parametric Curves
- Candidate Test
- Combining Differentiation Rules
- Combining Functions
- Continuity
- Continuity Over an Interval
- Convergence Tests
- Cost and Revenue
- Density and Center of Mass
- Derivative Functions
- Derivative of Exponential Function
- Derivative of Inverse Function
- Derivative of Logarithmic Functions
- Derivative of Trigonometric Functions
- Derivatives
- Derivatives and Continuity
- Derivatives and the Shape of a Graph
- Derivatives of Inverse Trigonometric Functions
- Derivatives of Polar Functions
- Derivatives of Sec, Csc and Cot
- Derivatives of Sin, Cos and Tan
- Determining Volumes by Slicing
- Direction Fields
- Disk Method
- Divergence Test
- Eliminating the Parameter
- Euler's Method
- Evaluating a Definite Integral
- Evaluation Theorem
- Exponential Functions
- Finding Limits
- Finding Limits of Specific Functions
- First Derivative Test
- Function Transformations
- General Solution of Differential Equation
- Geometric Series
- Growth Rate of Functions
- Higher-Order Derivatives
- Hydrostatic Pressure
- Hyperbolic Functions
- Implicit Differentiation Tangent Line
- Implicit Relations
- Improper Integrals
- Indefinite Integral
- Indeterminate Forms
- Initial Value Problem Differential Equations
- Integral Test
- Integrals of Exponential Functions
- Integrals of Motion
- Integrating Even and Odd Functions
- Integration Formula
- Integration Tables
- Integration Using Long Division
- Integration of Logarithmic Functions
- Integration using Inverse Trigonometric Functions
- Intermediate Value Theorem
- Inverse Trigonometric Functions
- Jump Discontinuity
- Lagrange Error Bound
- Limit Laws
- Limit of Vector Valued Function
- Limit of a Sequence
- Limits
- Limits at Infinity
- Limits of a Function
- Linear Approximations and Differentials
- Linear Differential Equation
- Linear Functions
- Logarithmic Differentiation
- Logarithmic Functions
- Logistic Differential Equation
- Maclaurin Series
- Manipulating Functions
- Maxima and Minima
- Maxima and Minima Problems
- Mean Value Theorem for Integrals
- Models for Population Growth
- Motion Along a Line
- Motion in Space
- Natural Logarithmic Function
- Net Change Theorem
- Newton's Method
- Nonhomogeneous Differential Equation
- One-Sided Limits
- Optimization Problems
- P Series
- Particle Model Motion
- Particular Solutions to Differential Equations
- Polar Coordinates
- Polar Coordinates Functions
- Polar Curves
- Population Change
- Power Series
- Ratio Test
- Removable Discontinuity
- Riemann Sum
- Rolle's Theorem
- Root Test
- Second Derivative Test
- Separable Equations
- Simpson's Rule
- Solid of Revolution
- Solutions to Differential Equations
- Surface Area of Revolution
- Symmetry of Functions
- Tangent Lines
- Taylor Polynomials
- Taylor Series
- Techniques of Integration
- The Fundamental Theorem of Calculus
- The Mean Value Theorem
- The Power Rule
- The Squeeze Theorem
- The Trapezoidal Rule
- Theorems of Continuity
- Trigonometric Substitution
- Vector Valued Function
- Vectors in Calculus
- Vectors in Space
- Washer Method
- Decision Maths
- Geometry
- 2 Dimensional Figures
- 3 Dimensional Vectors
- 3-Dimensional Figures
- Altitude
- Angles in Circles
- Arc Measures
- Area and Volume
- Area of Circles
- Area of Circular Sector
- Area of Parallelograms
- Area of Plane Figures
- Area of Rectangles
- Area of Regular Polygons
- Area of Rhombus
- Area of Trapezoid
- Area of a Kite
- Composition
- Congruence Transformations
- Congruent Triangles
- Convexity in Polygons
- Coordinate Systems
- Dilations
- Distance and Midpoints
- Equation of Circles
- Equilateral Triangles
- Figures
- Fundamentals of Geometry
- Geometric Inequalities
- Geometric Mean
- Geometric Probability
- Glide Reflections
- HL ASA and AAS
- Identity Map
- Inscribed Angles
- Isometry
- Isosceles Triangles
- Law of Cosines
- Law of Sines
- Linear Measure and Precision
- Median
- Parallel Lines Theorem
- Parallelograms
- Perpendicular Bisector
- Plane Geometry
- Polygons
- Projections
- Properties of Chords
- Proportionality Theorems
- Pythagoras Theorem
- Rectangle
- Reflection in Geometry
- Regular Polygon
- Rhombuses
- Right Triangles
- Rotations
- SSS and SAS
- Segment Length
- Similarity
- Similarity Transformations
- Special quadrilaterals
- Squares
- Surface Area of Cone
- Surface Area of Cylinder
- Surface Area of Prism
- Surface Area of Sphere
- Surface Area of a Solid
- Surface of Pyramids
- Symmetry
- Translations
- Trapezoids
- Triangle Inequalities
- Triangles
- Using Similar Polygons
- Vector Addition
- Vector Product
- Volume of Cone
- Volume of Cylinder
- Volume of Pyramid
- Volume of Solid
- Volume of Sphere
- Volume of prisms
- Mechanics Maths
- Acceleration and Time
- Acceleration and Velocity
- Angular Speed
- Assumptions
- Calculus Kinematics
- Coefficient of Friction
- Connected Particles
- Constant Acceleration
- Constant Acceleration Equations
- Converting Units
- Force as a Vector
- Kinematics
- Newton's First Law
- Newton's Law of Gravitation
- Newton's Second Law
- Newton's Third Law
- Projectiles
- Pulleys
- Resolving Forces
- Statics and Dynamics
- Tension in Strings
- Variable Acceleration
- Probability and Statistics
- Bar Graphs
- Basic Probability
- Charts and Diagrams
- Conditional Probabilities
- Continuous and Discrete Data
- Frequency, Frequency Tables and Levels of Measurement
- Independent Events Probability
- Line Graphs
- Mean Median and Mode
- Mutually Exclusive Probabilities
- Probability Rules
- Probability of Combined Events
- Quartiles and Interquartile Range
- Systematic Listing
- Pure Maths
- ASA Theorem
- Absolute Value Equations and Inequalities
- Addition and Subtraction of Rational Expressions
- Addition, Subtraction, Multiplication and Division
- Algebra
- Algebraic Fractions
- Algebraic Notation
- Algebraic Representation
- Analyzing Graphs of Polynomials
- Angle Measure
- Angles
- Angles in Polygons
- Approximation and Estimation
- Area and Circumference of a Circle
- Area and Perimeter of Quadrilaterals
- Area of Triangles
- Arithmetic Sequences
- Average Rate of Change
- Bijective Functions
- Binomial Expansion
- Binomial Theorem
- Chain Rule
- Circle Theorems
- Circles
- Circles Maths
- Combination of Functions
- Combinatorics
- Common Factors
- Common Multiples
- Completing the Square
- Completing the Squares
- Complex Numbers
- Composite Functions
- Composition of Functions
- Compound Interest
- Compound Units
- Conic Sections
- Construction and Loci
- Converting Metrics
- Convexity and Concavity
- Coordinate Geometry
- Coordinates in Four Quadrants
- Cubic Function Graph
- Cubic Polynomial Graphs
- Data transformations
- Deductive Reasoning
- Definite Integrals
- Deriving Equations
- Determinant of Inverse Matrix
- Determinants
- Differential Equations
- Differentiation
- Differentiation Rules
- Differentiation from First Principles
- Differentiation of Hyperbolic Functions
- Direct and Inverse proportions
- Disjoint and Overlapping Events
- Disproof by Counterexample
- Distance from a Point to a Line
- Divisibility Tests
- Double Angle and Half Angle Formulas
- Drawing Conclusions from Examples
- Ellipse
- Equation of Line in 3D
- Equation of a Perpendicular Bisector
- Equation of a circle
- Equations
- Equations and Identities
- Equations and Inequalities
- Estimation in Real Life
- Euclidean Algorithm
- Evaluating and Graphing Polynomials
- Even Functions
- Exponential Form of Complex Numbers
- Exponential Rules
- Exponentials and Logarithms
- Expression Math
- Expressions and Formulas
- Faces Edges and Vertices
- Factorials
- Factoring Polynomials
- Factoring Quadratic Equations
- Factorising expressions
- Factors
- Finding Maxima and Minima Using Derivatives
- Finding Rational Zeros
- Finding the Area
- Forms of Quadratic Functions
- Fractional Powers
- Fractional Ratio
- Fractions
- Fractions and Decimals
- Fractions and Factors
- Fractions in Expressions and Equations
- Fractions, Decimals and Percentages
- Function Basics
- Functional Analysis
- Functions
- Fundamental Counting Principle
- Fundamental Theorem of Algebra
- Generating Terms of a Sequence
- Geometric Sequence
- Gradient and Intercept
- Graphical Representation
- Graphing Rational Functions
- Graphing Trigonometric Functions
- Graphs
- Graphs and Differentiation
- Graphs of Common Functions
- Graphs of Exponents and Logarithms
- Graphs of Trigonometric Functions
- Greatest Common Divisor
- Growth and Decay
- Growth of Functions
- Highest Common Factor
- Hyperbolas
- Imaginary Unit and Polar Bijection
- Implicit differentiation
- Inductive Reasoning
- Inequalities Maths
- Infinite geometric series
- Injective functions
- Instantaneous Rate of Change
- Integers
- Integrating Polynomials
- Integrating Trig Functions
- Integrating e^x and 1/x
- Integration
- Integration Using Partial Fractions
- Integration by Parts
- Integration by Substitution
- Integration of Hyperbolic Functions
- Interest
- Inverse Hyperbolic Functions
- Inverse Matrices
- Inverse and Joint Variation
- Inverse functions
- Iterative Methods
- Law of Cosines in Algebra
- Law of Sines in Algebra
- Laws of Logs
- Limits of Accuracy
- Linear Expressions
- Linear Systems
- Linear Transformations of Matrices
- Location of Roots
- Logarithm Base
- Logic
- Lower and Upper Bounds
- Lowest Common Denominator
- Lowest Common Multiple
- Math formula
- Matrices
- Matrix Addition and Subtraction
- Matrix Determinant
- Matrix Multiplication
- Metric and Imperial Units
- Misleading Graphs
- Mixed Expressions
- Modulus Functions
- Modulus and Phase
- Multiples of Pi
- Multiplication and Division of Fractions
- Multiplicative Relationship
- Multiplying and Dividing Rational Expressions
- Natural Logarithm
- Natural Numbers
- Notation
- Number
- Number Line
- Number Systems
- Numerical Methods
- Odd functions
- Open Sentences and Identities
- Operation with Complex Numbers
- Operations with Decimals
- Operations with Matrices
- Operations with Polynomials
- Order of Operations
- Parabola
- Parallel Lines
- Parametric Differentiation
- Parametric Equations
- Parametric Integration
- Partial Fractions
- Pascal's Triangle
- Percentage
- Percentage Increase and Decrease
- Percentage as fraction or decimals
- Perimeter of a Triangle
- Permutations and Combinations
- Perpendicular Lines
- Points Lines and Planes
- Polynomial Graphs
- Polynomials
- Powers Roots And Radicals
- Powers and Exponents
- Powers and Roots
- Prime Factorization
- Prime Numbers
- Problem-solving Models and Strategies
- Product Rule
- Proof
- Proof and Mathematical Induction
- Proof by Contradiction
- Proof by Deduction
- Proof by Exhaustion
- Proof by Induction
- Properties of Exponents
- Proportion
- Proving an Identity
- Pythagorean Identities
- Quadratic Equations
- Quadratic Function Graphs
- Quadratic Graphs
- Quadratic functions
- Quadrilaterals
- Quotient Rule
- Radians
- Radical Functions
- Rates of Change
- Ratio
- Ratio Fractions
- Rational Exponents
- Rational Expressions
- Rational Functions
- Rational Numbers and Fractions
- Ratios as Fractions
- Real Numbers
- Reciprocal Graphs
- Recurrence Relation
- Recursion and Special Sequences
- Remainder and Factor Theorems
- Representation of Complex Numbers
- Rewriting Formulas and Equations
- Roots of Complex Numbers
- Roots of Polynomials
- Roots of Unity
- Rounding
- SAS Theorem
- SSS Theorem
- Scalar Triple Product
- Scale Drawings and Maps
- Scale Factors
- Scientific Notation
- Second Order Recurrence Relation
- Sector of a Circle
- Segment of a Circle
- Sequences
- Sequences and Series
- Series Maths
- Sets Math
- Similar Triangles
- Similar and Congruent Shapes
- Simple Interest
- Simplifying Fractions
- Simplifying Radicals
- Simultaneous Equations
- Sine and Cosine Rules
- Small Angle Approximation
- Solving Linear Equations
- Solving Linear Systems
- Solving Quadratic Equations
- Solving Radical Inequalities
- Solving Rational Equations
- Solving Simultaneous Equations Using Matrices
- Solving Systems of Inequalities
- Solving Trigonometric Equations
- Solving and Graphing Quadratic Equations
- Solving and Graphing Quadratic Inequalities
- Special Products
- Standard Form
- Standard Integrals
- Standard Unit
- Straight Line Graphs
- Substraction and addition of fractions
- Sum and Difference of Angles Formulas
- Sum of Natural Numbers
- Surds
- Surjective functions
- Tables and Graphs
- Tangent of a Circle
- The Quadratic Formula and the Discriminant
- Transformations
- Transformations of Graphs
- Translations of Trigonometric Functions
- Triangle Rules
- Triangle trigonometry
- Trigonometric Functions
- Trigonometric Functions of General Angles
- Trigonometric Identities
- Trigonometric Ratios
- Trigonometry
- Turning Points
- Types of Functions
- Types of Numbers
- Types of Triangles
- Unit Circle
- Units
- Variables in Algebra
- Vectors
- Verifying Trigonometric Identities
- Writing Equations
- Writing Linear Equations
- Statistics
- Bias in Experiments
- Binomial Distribution
- Binomial Hypothesis Test
- Bivariate Data
- Box Plots
- Categorical Data
- Categorical Variables
- Central Limit Theorem
- Chi Square Test for Goodness of Fit
- Chi Square Test for Homogeneity
- Chi Square Test for Independence
- Chi-Square Distribution
- Combining Random Variables
- Comparing Data
- Comparing Two Means Hypothesis Testing
- Conditional Probability
- Conducting a Study
- Conducting a Survey
- Conducting an Experiment
- Confidence Interval for Population Mean
- Confidence Interval for Population Proportion
- Confidence Interval for Slope of Regression Line
- Confidence Interval for the Difference of Two Means
- Confidence Intervals
- Correlation Math
- Cumulative Frequency
- Data Analysis
- Data Interpretation
- Discrete Random Variable
- Distributions
- Dot Plot
- Empirical Rule
- Errors in Hypothesis Testing
- Estimator Bias
- Events (Probability)
- Frequency Polygons
- Generalization and Conclusions
- Geometric Distribution
- Histograms
- Hypothesis Test for Correlation
- Hypothesis Test of Two Population Proportions
- Hypothesis Testing
- Inference for Distributions of Categorical Data
- Inferences in Statistics
- Large Data Set
- Least Squares Linear Regression
- Linear Interpolation
- Linear Regression
- Measures of Central Tendency
- Methods of Data Collection
- Normal Distribution
- Normal Distribution Hypothesis Test
- Normal Distribution Percentile
- Point Estimation
- Probability
- Probability Calculations
- Probability Distribution
- Probability Generating Function
- Quantitative Variables
- Quartiles
- Random Variables
- Randomized Block Design
- Residual Sum of Squares
- Residuals
- Sample Mean
- Sample Proportion
- Sampling
- Sampling Distribution
- Scatter Graphs
- Single Variable Data
- Skewness
- Standard Deviation
- Standard Normal Distribution
- Statistical Graphs
- Statistical Measures
- Stem and Leaf Graph
- Sum of Independent Random Variables
- Survey Bias
- Transforming Random Variables
- Tree Diagram
- Two Categorical Variables
- Two Quantitative Variables
- Type I Error
- Type II Error
- Types of Data in Statistics
- Venn Diagrams

Mathematicians often use the known properties of different shapes to help them solve problems. In this article, we will explore the classic and common three-sided shape, the triangle. You may be surprised to see an article dedicated entirely to triangles, but this is a broad topic with many interesting details to uncover! Let's start by defining what we even mean by a triangle.

The term "triangle" itself is a combination of two words: tri (meaning three) and angle (a space formed by the meeting of two lines). We can use this understanding to approach our definition of a triangle:

Triangles are shapes with three sides. Because they have three sides, they also have three angles.

Triangles used to be referred to as trigons. However, this term has mostly been replaced with the more common term, triangle.

Now, let's illustrate what we mean by a triangle. Every triangle has three sides and three edges or corners which are known as vertices.

The figure below shows a triangle, . We can write to denote the triangle . Now, has three vertices A, B, and C. It also has three sides: AB, BC, and CA.

Example of a triangle - StudySmarter Originals

As illustrated in the above image, triangles have three angles. If we were to cut each of these angles out of the triangle and line them up next to each other, we could notice that all three angles would form a straight line. Recall that angles on a straight line sum to 180 degrees. Therefore, we can say that angles in a triangle add up to 180 degrees.

Therefore, if the three angles of the triangle are , and , we can say that:

This is an important fact, as we can use it to help determine missing angles in a triangle. We will do this in the following example:

Suppose we have a triangle with angles and . Work out the third angle.

Solution:

Let's denote the missing angle by . Since the three angles in a triangle add up to , we can say:

Therefore,

.

Subtracting from both sides, we obtain:

Therefore, the missing angle is .** **

Now, we will talk about finding the area of a triangle.

The area of a shape is the space that it takes up. It is measured in square units (i.e., m^{2} or ft^{2}).

There is a formula that allows us to work out the area of any given triangle. It is:

So, all we need to know is the base and the height to work out the triangle's area. When we refer to the height, we are talking about the **perpendicular** **height** as measured from the base. So, the height and base should be at right angles** **to each other, as shown in the diagram below.

In the triangle ACB, we have the base of and the height of . We can also see that is perpendicular to (). So, if we measured their lengths, we could work out the area of this triangle using the formula.

Recall that the area is measured in square units. So, if the height and the base are measured in centimeters (), the area would be measured in centimeters squared ().

Suppose the base of a triangle is and the height is . Work out the area of the triangle.

Solution:

Using the fact that:

We can say that:

Therefore, the area of this triangle is .

In addition to the area of triangles, we are often asked to work out the perimeter as well. The perimeter is the sum of all of the lengths of the triangle's sides. So, to obtain the perimeter, we need to add up these side lengths.

The formula for a triangle's perimeter can be written as:

Where , , and are the lengths of each of the three sides of the triangle. Let's take a look at how to use this formula in an example problem.

If we have a triangle with side lengths , , and , what would the perimeter be?

Solution:

Using the formula for the perimeter, we have that:

So, the perimeter of this triangle would be .

There are different types of triangles that are characterized by specific properties. We will discuss the properties of four types in more detail, including:

- The equilateral triangle
- The isosceles triangle
- The scalene triangle
- The right-angled triangle

Equilateral triangles consist of three equal sides and three equal angles, which helps to explain the name of ** equil**ateral. Recall from earlier that the three angles in a triangle sum up to . Since the equilateral triangle has three equal angles, we can say that each angle is , as calculated by: . If we have a triangle where we know each angle is equal to , we can say that it is an equilateral triangle.

The figure below shows an example of an equilateral triangle. Note that the ticks on each side of this triangle are there to show that each of the sides is equal in length.

Isosceles is a fun word to say, but what does it mean? Isosceles triangles are triangles with two equal sides and hence two equal angles. So, a useful characteristic of isosceles triangles is that we only need to know the size of one of the angles to be able to work out the other two! We will look at an example of this later on.

Below is an example of an isosceles triangle. Note that the ticks on two of the sides show that these two sides are equal in length.

So, we know that an equilateral triangle has three equal sides, and an isosceles triangle has two equal sides. Can you guess what a scalene triangle is? Scalene triangles have no equal sides and no equal angles.

Below is an example of a scalene triangle. This time there are no ticks on any of the sides because none of the sides are the same!

We also have a special type of triangle, which is instead classified by the properties of its angles. If one of the triangle's angles is a right angle, meaning it is, the triangle is a right-angled triangle. This type of triangle is particularly useful in the study of Trigonometry. Below is an example of a right-angled triangle:

Now, if we have a right-angled triangle, by definition, the triangle is also either an isosceles or scalene triangle. Take a look at the below example to see why:

Suppose the three angles of a triangle are , , and . In this case, since one of the angles is a right angle, it is a right-angled triangle. However, since all three of the angles are different, it is also a scalene triangle.

Now, suppose we have another right-angled triangle with angles of , , and . In this case, it is a right-angled triangle and also an isosceles triangle because two of the angles are the same.

It's not possible for a triangle to be both equilateral and right-angled, however. To fit the definition of an equilateral triangle, all of the angles would need to be the same, and to fit the definition of a right-angled triangle, one of the angles would need to be . This means that the triangle would need to have three angles of, like so:

However, the angles of a triangle have to add up to ! Thus, right-angled triangles can also be classified as either isosceles or scalene.

An important and well-known theorem about right-angled triangles is the Pythagorean theorem, which relates to the sides of right-angled triangles. This theorem is very useful because it enables us to find the length of a missing side of a right-angled triangle if we already know the other two sides.

For the right-angled triangle above, with sides labelled as, , and , the theorem gives the following formula:

The side labelled as is known as the **hypotenuse** of the triangle. Let's now take a look at a quick example to see how the Pythagorean theorem works.

Suppose we have the below triangle. Work out the size of the size labelled :

** **** **

Solution:

For this right-angled triangle, we can see that is the hypotenuse, so we label it as to fit our formula. So, let's now label the other sides as and .

Applying the Pythagorean theorem, we can say that:

Now, substituting in our values of ,, and , we get:

Taking the square root of both sides,

Therefore, the length of the triangle's hypotenuse is .

When we have integer values for all three sides of a right angle, the side lengths are together known as a Pythagorean Triple.

We will now go through some example problems concerning triangles to test your understanding!

A triangle has two angles and . Show that this triangle is right-angled.** **

Solution:

Let's first define the missing angle to be . Since angles in a triangle sum to , we have:

Therefore,

Subtracting from both sides, we obtain:

.

Thus, the missing angle is , which is a right angle. From this, we know that it is a right-angled triangle.

In the below isosceles triangle , we know that and . Work out the size of the other two angles.** **

** **

Solution:

Since **, **we know that. Now, since angles in a triangle sum to , we can say:

.

Therefore,

Subtracting from both sides, we obtain:

So, and

In the below triangle, is equilateral and . Work out the size of and .** **

Solution:

Firstly, since is equilateral, we can say that each of the angles within it are . So, .** **

Since angles on a straight line sum to , we have:

With this information, we can work out :

Subtracting from both sides, we get:

.

So and .

A given isosceles triangle has an angle of . Work out two possibilities for the sizes of its other two angles.** **

Solution:

Firstly, since it is isosceles, two of the angles must be the same. If one of the angles is , then one of the other angles could be as well to meet this property. In this case, that would make the third and last angle by the following calculation:

So, our isosceles triangle could have angles: .

Another possible scenario is that only one of the angles is . In this case, the other two angles would need to be the same. Since angles in a triangle sum to , the other two angles would need to sum to:

.

Since the two remaining angles are both the same, they would each be:

.

Therefore, our isosceles triangle could also have angles: .

So, the two possibilities are: or .

- Triangles are shapes with three sides and three angles.
- Every triangle has three sides and three edges or corners which are known as vertices.
- The three angles in a triangle add up to 180 degrees.
- We have a formula for the area of a triangle as follows:
- The four main types of triangles are: equilateral, isosceles, scalene, and right-angled.
- Equilateral triangles consist of three equal sides and three equal angles.
- Isosceles triangles are triangles with two equal sides and two equal angles.
- Scalene triangles have no equal sides and no equal angles.

A triangle is a shape with three sides.

The area of any triangle can be computed by multiplying 1/2 by the base, multiplied by height.

The internal angles in a triangle sum to 180 degrees.

To find the perimeter of a triangle, add up the lengths of all of the sides of the triangle.

More about Triangles

Be perfectly prepared on time with an individual plan.

Test your knowledge with gamified quizzes.

Create and find flashcards in record time.

Create beautiful notes faster than ever before.

Have all your study materials in one place.

Upload unlimited documents and save them online.

Identify your study strength and weaknesses.

Set individual study goals and earn points reaching them.

Stop procrastinating with our study reminders.

Earn points, unlock badges and level up while studying.

Create flashcards in notes completely automatically.

Create the most beautiful study materials using our templates.

Sign up to highlight and take notes. It’s 100% free.