Question

the figure shows two triangles with two pairs of congruent angles. if ac = 10 units, what is ad?
a. 4 units
b. 6.5 units
c. 10 units
d. 12 units

Explanation:

Step1: Identify Congruent Triangles

The two triangles share side \( AB \), have two pairs of congruent angles (implied by the markings and the figure), so by the Angle - Angle - Side (AAS) or Angle - Side - Angle (ASA) congruence criterion, the triangles \( \triangle ABC \) and \( \triangle ABD \) are congruent.

Step2: Use Congruence Property

In congruent triangles, corresponding sides are equal. Since \( AC \) and \( AD \) are corresponding sides of the congruent triangles, \( AD=AC \).

Step3: Substitute the Value of \( AC \)

Given \( AC = 10 \) units, so \( AD=10 \) units.

Answer:

C. 10 units