Question

Are the triangles similar? How do you know? A. yes, by SAS B. yes, by SSS C. yes, by AA D. no

Answer 1

no, because 30.4+84.6+66=181
the sum of a triangle=180
so they are not similar.

Answer 2

Option D is correct.

No, the triangles are not similar.

Explanation:

AA postulates states that two triangles are similar if they have two corresponding angles equal.

Labelled the diagram as shown below:

We know that sum of all the measure of the angles in a triangle is 180 degree.

In triangle ABC:

`\angle A + \angle B + \angle C = 180^(\circ)`

⇒
`30.4^(\circ)+84.6^(\circ)+\angle C = 180^(\circ)`

⇒
`115^(\circ)+\angle C = 180^(\circ)`

Subtract 115 degree from both sides we get;

⇒
`\angle C = 65^(\circ)`

In triangle ABC and PQR

`\angle A = \angle Q = 84.6^(\circ)`

`\angle C \\eq \angle R`

i.e
`65^(\circ)\\eq 66^(\circ)`

⇒These triangles does not satisfy the AA postulates

Therefore, the given triangles are not similar.