Question

Select the postulate or theorem that you can use to conclude that the triangles are similar

AA Similarity Postulate

SAS Similarity Theorem

SSS Similarity Theorem

Answer 1

4/2 = 6/3 =2
<M=<M

answer
SAS Similarity Theorem

Answer 2

(B) SAS Similarity Theorem

Explanation:

Given: The two triangles GMK and PMS and GM=3, MS=6, PM=4 and MK=2

To find: The similarity postulate in order to prove two triangles are similar.

Solution: From the two triangles,using the proportionality condition, we have

`(GM)/(MS)=(KM)/(MP)`

Substituting the given values,. we get

`(3)/(6)=(2)/(4)=(1)/(2)`

Thus, the proportionality condition holds.

Now, from ΔGMK and ΔPMS, we have

`(GM)/(MS)=(KM)/(MP)` (Proved above)

∠GMK=∠PMS (Vertically opposite angles)

Hence, by SAS similarity theorem, ΔGMK is similar to ΔPMS.

Hence, option (B) is correct.