Questions: What are the corresponding parts of the figures below? Select all that apply. angle M is equivalent to angle X angle N equals angle W line segment NM is congruent to line segment XV angle L is congruent to angle V

What are the corresponding parts of the figures below? Select all that apply.
angle M is equivalent to angle X
angle N equals angle W
line segment NM is congruent to line segment XV
angle L is congruent to angle V

Transcript text: What are the corresponding parts of the figures below? Select all that apply. $\angle M \equiv \angle X$ $\angle N=\angle W$ $\overline{N M} \cong \overline{X V}$ $\angle L \cong \angle V$

Solution

Solution Steps

Step 1: Analyze the angles

The given triangles have the following angles: Triangle LMN: $ \angle L = 36^\circ $, $ \angle M = 64^\circ $, $ \angle N = 80^\circ $ Triangle VWX: $ \angle V = 36^\circ $, $ \angle X = 64^\circ $, $ \angle W = 80^\circ $

Step 2: Analyze the sides

The given triangles have the following sides: Triangle LMN: LM = 41 in, MN = 24 in, LN = 37 in Triangle VWX: VX = 41 in, XW = 24 in, VW = 37 in

Step 3: Determine corresponding parts

From the angles, we have the following equivalences: $ \angle L \cong \angle V $ (Both are 36°) $ \angle M \cong \angle X $ (Both are 64°) $ \angle N \cong \angle W $ (Both are 80°)

From the sides, we have the following congruences: $ \overline{LM} \cong \overline{VX} $ (Both are 41 in) $ \overline{MN} \cong \overline{XW} $ (Both are 24 in) $ \overline{LN} \cong \overline{VW} $ (Both are 37 in)

Final Answer

The corresponding parts are: $ \angle M \cong \angle X $, $ \angle N \cong \angle W $, and $ \angle L \cong \angle V $. Specifically, the correct options from the given choices are: $ \angle M \equiv \angle X $ $ \angle N \cong \angle W $ $ \angle L \cong \angle V $

$ \overline{NM} \cong \overline{XW} $, not $ \overline{XV} $. Thus, $ \overline{N M} \cong \overline{X V} $ is not a corresponding part.

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