Question

Determine if the triangles, ΔZBX and ΔNBG, are similar. If so, identify the similarity criterion.

Answer 1

Answer:

B

Step-by-step explanation:

Consider triangles ZBX and NBG. In these triangles, angles ZBX and NBG are congruent as vertical angles (two opposite angles when two lines intersect).

From the diagram,

$\dfrac{XB}{BG}=\dfrac{5}{15}=\dfrac{1}{3}\\ \\\dfrac{ZB}{BN}=\dfrac{4}{12}=\dfrac{1}{3}$

Hence,

$\dfrac{XB}{BG}=\dfrac{ZB}{BN}$

Therefore, triangles ZBX and NBG are similar by SAS similarity theorem.

SAS Similarity Theorem states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.