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

Answer:

Option D is correct.

No, the triangles are not similar.

Step-by-step 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

$\angle A = \angle Q = 84.6^{\circ}$

$\angle C \neq \angle R$

i.e $65^{\circ}\neq 66^{\circ}$

⇒These triangles does not satisfy the AA postulates

Therefore, the given triangles are not similar.

Answer 2

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