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Q9.

Expert-verifiedFound in: Page 120

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)**.

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

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).

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).

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