Question

Triangles A C B and M Q R are shown. Sides A B and M R are congruent. Angles C A B and M R Q are 42 degrees. Angle C B A is 53 degrees. Angle M Q R is 85 degrees.
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, AngleB is not congruent to AngleQ.
No, the congruent sides do not correspond.
2 triangles are connected at one side. The triangles have 2 congruent sides and 1 congruent angle. The first triangle is rotated and then translated down to form the second triangle.

Answer 1

By ASA postulate it can be say that the triangle ABC and triangle MRQ are congruent

What is Angle Sum Property?

The sum of all three angles(interior) of a triangle is 180 degrees, and the exterior angle of a triangle measures the same as the sum of its two opposite interior angles.

Using Angle Sum Property, in ΔMRQ

<M + <R + <Q= 180

<M + 42 + 85 = 180

<M = 180 -42

<M= 53°

Now, In ΔMRQ and ΔABC  

<A= <R ,

<B = <M

AB = MR

Hence, By ASA criteria ΔMRQ ≅ ΔABC  

Learn more about this concept here:

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