Question

Determine whether the triangles are similar. If so, what is the similarity statement and the postulate or theorem used?

1) triangleTRS ~ triangleTPQ; SSS ~
2) triangleTRS ~ triangleTPQ; SAS ~
3) triangleTRS ~ trianglePQR; SAS~
4) The triangles are not similar.
need help with this one!!! thanks.

Answer 1

2) triangleTRS ~ triangleTPQ; SAS ~

Explanation:

`TR = TP + PR = 42 + 6 = 48\\</p><p>TS = TQ + QS = 28 + 4 = 32\\</p><p>In \:\triangle TRS\: and \:\triangle TPQ\\</p><p>(TR)/(TP) = (48)/(42) = (8)/(7) ....(1)\\\\</p><p>\angle RTS \cong \angle PTQ.. (common \: \angle)... (2)\\\\</p><p>(TS)/(TQ) = (32)/(28) = (8)/(7) ....(3)\\\\`

From equations (1), (2) & (3) it is obvious that:

`\therefore \triangle TRS \sim\triangle TPQ... (SAS \: Postulate)`