Question

Triangles RST and XYZ are drawn below. If RS= 6, ST=14, XY = 9, YZ=21, and ZSZY, is ARST similar to AXYZ? Justify your answer.

Answer 1

yes, ∆RST ~ ∆XYZ

Explanation:

You want to know if ∆RST is similar to ∆XYZ when RS=6, ST=14, XY=9, YZ=21 and ∠S≅∠Y.

SAS similarity

Two triangles are similar by the SAS theorem if corresponding sides have the same ratio, and the angles between them are congruent.

Application

Corresponding sides are ...

RS : XY = 6 : 9 = 2 : 3

ST : YZ = 14 : 21 = 2 : 3 . . . . same ratio

The angles between them are ...

∠S, ∠Y . . . . . given as congruent

Corresponding sides have the same ratios, and the angles between them are congruent, so the triangles are similar.