Question

geometry unit 4 triangle congruence review
name:
date:

1. what theorem proves that

$\triangle mnl\cong\triangle jkl$?
a) angle - angle - side
b) side - angle - side
c) hypotenuse - leg
d) angle - side - angle

1. select all the true statements

about the figure below.
$\circ\triangle xvw\cong\triangle ywv$
$\circ\overline{xv}\cong\overline{wy}$
$\circ\angle xvw\cong\angle xvz$
$\circ\triangle zxv\cong\triangle xvw$
$\circ\angle xyw\cong\angle wvx$
$\circ\overline{xw}\cong\overline{xv}$

1. what is the $m\angle ebc$?

$m\angle ebc =$

1. what is $ad$?

a) 60
b) 20
c) 23
d) 10

Explanation:

1.

Step1: Identify vertical angles

Vertical angles are equal. So \( \angle MLN=\angle JLK \).

Step2: Analyze given congruent sides

\( ML = JL \) (given as marked equal) and \( LN=LK \) (given as marked equal).

Step3: Use congruence theorem

By the Side - Angle - Side (SAS) congruence theorem (two sides and the included angle), \( \triangle MNL\cong\triangle JKL \).

Step1: Check \( \triangle XVW\cong\triangle YWV \)

By Side - Side - Side (SSS) (if \( XV = YW \), \( VW=VW \), \( XW = YV \) (assuming from markings)), \( \triangle XVW\cong\triangle YWV \).

Step2: Check \( \overline{XV}\cong\overline{WY} \)

From \( \triangle XVW\cong\triangle YWV \), corresponding parts \( \overline{XV}\cong\overline{WY} \).

Step3: Check \( \angle XYW\cong\angle WVX \)

From \( \triangle XVW\cong\triangle YWV \), corresponding angles \( \angle XYW\cong\angle WVX \).

Step1: Use exterior angle property

The exterior angle \( \angle EBC \) of a triangle. Let's assume the triangle where we can use angle sum or exterior angle relations. If we consider the relevant triangle, and using angle sum in a triangle (sum of angles in a triangle is \( 180^{\circ} \)). Suppose we have angles related to \( \angle EBC \). If we assume some known angles (from the figure's markings), and using the fact that \( \angle EBC = 180^{\circ}- 80^{\circ}=100^{\circ} \) (if it's a linear - pair or based on triangle angle sum with given angles).

Answer:

b) Side - Angle - Side

2.