Question

Determine if triangle OPQ and triangle RST are or are not similar, and, if they are, state which triangle similarity shortcut (AA, SSS, SAS) you can use to prove it. Show your work below proving that the triangles met the shortcut's criteria (Note that figures are NOT necessarily drawn to scale.)​

Answer 1

SAS Similarity

Explanation:

ΔOPQ similar to ΔRST

∠Q = ∠T

OQ : RT = 28 : 84 = 1 : 3

QP : TS = 16 : 48 = 1 : 3

The measures of two sides of ΔOPQ are proportional to the measure of two side of ΔRST and their included angles are congruent. The triangles are similar by SAS Similarity.