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Q9.

Expert-verified
Found in: Page 120

### Geometry

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

# Suppose $\Delta \text{LXR}\cong \Delta \text{FNE}$. List six congruence that can be justified by the following reason: Corr. Parts of $\cong \Delta$ are $\cong$.

Six congruence are:

$\mathbf{\text{LX}}\mathbf{\cong }\mathbf{\text{FN,XR}}\mathbf{\cong }\mathbf{\text{NE,LR}}\mathbf{\cong }\mathbf{\text{FE}}$ (Corresponding sides of the congruent triangle triangles are congruent).

role="math" localid="1638272678591" $\mathbf{\angle }\mathbf{\text{L}}\mathbf{\cong }\mathbf{\angle }\mathbf{\text{F,}}\mathbf{\angle }\mathbf{\text{X}}\mathbf{\cong }\mathbf{\angle }\mathbf{\text{N,}}\mathbf{\angle }\mathbf{\text{R}}\mathbf{\cong }\mathbf{\angle }\mathbf{\text{E}}$ (Corresponding angles of the congruent triangle triangles are congruent).

See the step by step solution

## Step 1. State the definition of congruency.

Two figures or objects are congruent if they have the same shape and size.

## Step 2. State the explanation.

It is given that corresponding parts of congruent triangles are congruent.

Corresponding parts means corresponding angles and corresponding sides of the congruent triangles.

As $\Delta LXR\cong \Delta FNE$, then,

$LX\cong FN,XR\cong NE,LR\cong FE$ (Corresponding sides of the congruent triangle triangles are congruent).

$\angle L\cong \angle F,\angle X\cong \angle N,\angle R\cong \angle E$ (Corresponding sides of the congruent triangle triangles are congruent).

## Step 3. State the conclusion.

Therefore, the six congruences are:

$LX\cong FN,XR\cong NE,LR\cong FE$ (Corresponding sides of the congruent triangle triangles are congruent).

$\angle L\cong \angle F,\angle X\cong \angle N,\angle R\cong \angle E$ (Corresponding sides of the congruent triangle triangles are congruent).