Question

Are the triangles congruent? Why or why not?

Yes, all the angles of each of the triangles are acute.
Yes, they are congruent by either ASA or AAS.
No, B is not congruent to Q.
No, the congruent sides do not correspond.

Answer 1

They're congruent by ASA! (:
Which ASA stands for Angle Side Angle!
I hope all is well, and you pass! Good luck, rockstar! (: I genuinely wish you the best!

Answer 2

According to the ASA postulate it can be say that the triangle ABC and triangle MRQ are congruent because $\rm \angle A = \angle R$, $\rm \angle B = \angle M$, and sides, AB = MR.

Given :

• In triangle ABC, $\rm \angle A = 42^\circ \;and \;\angle B = 53^\circ$ .

• In triangle MRQ, $\rm \angle R = 42^\circ \;and \;\angle Q = 85^\circ$.
• Sides, AB = MR.

The sum of interior angles of a triangle is equal to $180^\circ$. Now, in triangle MRQ:

$\rm \angle M +\angle R +\angle Q =180^\circ$

$\rm \angle M +42^\circ + 85^\circ = 180^\circ$

$\rm \angle M = 180^\circ - 42^\circ-85^\circ$

$\rm \angle M = 53^\circ$

From triangle ABC and triangle MRQ, it can be say that:

$\rm \angle A = \angle R$,

$\rm \angle B = \angle M$,

Sides, AB = MR.

Therefore, according to the ASA postulate it can be concluded that the triangle ABC and triangle MRQ are congruent.

For more information, refer the link given below:

https://brainly.com/question/19673210