Question

question 4 of 10
david drew △pqr and △stu so that ∠p ≅ ∠s, pr = 12, su = 3, pq = 20, and st = 5. are △pqr and △stu similar? if so, identify the similarity postulate or theorem that applies.

a. cannot be determined
b. similar - sas
c. similar - aa
d. similar - sss

Explanation:

Step1: Check ratios of sides

Calculate the ratios of corresponding sides: $\frac{PR}{SU}=\frac{12}{3}=4$ and $\frac{PQ}{ST}=\frac{20}{5}=4$. So, $\frac{PR}{SU}=\frac{PQ}{ST}$.

Step2: Check included angle

We know $\angle P\cong\angle S$, which is the included angle between the sides we just compared (PR, PQ in $\triangle PQR$ and SU, ST in $\triangle STU$).

Step3: Apply SAS similarity

By the SAS (Side - Angle - Side) similarity theorem, if two sides of one triangle are in proportion to two sides of another triangle and the included angles are congruent, the triangles are similar. Here, two sides are proportional ($\frac{PR}{SU}=\frac{PQ}{ST}=4$) and the included angle ($\angle P\cong\angle S$) is congruent. So, $\triangle PQR\sim\triangle STU$ by SAS similarity.

Answer:

B. Similar - SAS