Question

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 $\cong$.

Short answer

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).

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).