Given ∠ABE = 45° and ∠EAB = 63° in ΔABE and∠MNP= 72° and ∠NMP = 63° in ΔMNP. Are the two triangles, ΔABE and ΔMNP similar? If so

Question

3 years ago

8

Given ∠ABE = 45° and ∠EAB = 63° in ΔABE and∠MNP= 72° and ∠NMP = 63° in ΔMNP. Are the two triangles, ΔABE and ΔMNP similar? If so

, by what criterion?
A) yes, by AA criterion
B) yes, by SAS criterion
C) yes, by SSA criterion
D) no, not possible to tell.

Mathematics

1 answer:

ivann1987 [24] · Answer 1 · 2022-04-21T06:59:42+03:00

A.) Yes, by AA criterion.

Triangle ABE have these angles:
∠ABE = 45° ; ∠EAB = 63° ; missing ∠ is 72°

Triangle MNP have these angles:
∠MNP = 72° ; ∠NMP = 63°; missing ∠ is 45°

AA criterion is "angle,angle" criterion. It means that the two triangles have at least two of their angles equal. Since a triangle have a total of 180°, when two of their angles are equal, the 3rd angle is also equal.

As you can see, both triangles have 45°, 63°, and 72° measurement of angles. Thus, they are similar.