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Q9

Expert-verified
Geometry
Found in: Page 35
Geometry

Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279

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Short Answer

Write each biconditional as two conditionals that are converses of each other.

Points are collinear if and only if they all lie in one line.

The two conditionals statement for given binomial is:

(a). If points are collinear, then they lie on the same line.

(b). If all points are in one line, then they are collinear.

See the step by step solution

Step by Step Solution

Step 1. Hypothesis and the conclusion.

The hypothesis and the conclusion of a conditional statement are where the hypothesis is the phrase immediately following by the word if and the conclusion is the phrase immediately following by the word then.

Step 2. Biconditional Statement.

The biconditional statement consists of a conditional statement along with its converse.

Step 3. State the conditionals.

As per the definition of conditionals, for the biconditional statement, “points are collinear if and only if they all lie in one line.” the two conditionals are:

(a). If points are collinear, then they lie on the same line.

(b). If all points are in one line, then they are collinear.

Both statements (a) and (b) are converses of each other.

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