Are the triangles congruent why or why not

The triangles are congruent by either Angle Side Angle (ASA) or Angle Angle Side (AAS).

Further Explanation:

The congruent triangles are those in which all the corresponding angles and the sides are equal.

There are many congruency rules and are as follows.

1. Angle Angle Side (AAS)

2. Angle Side Angle (ASA)

3. Side Side Side (SSS)

4. Side Angle Side (SAS)

Explanation:

The sum of all the angle of a triangle is {180^ \circ }180

∘

.

In triangle ABC the sum of all angle is {180^ \circ }180

∘

.

\begin{lgathered}\begin{aligned}\angle A+\angle B+\angle C&={180^\circ}\\{42^\circ}+{53^\circ }+\angle C&={180^\circ }\\\angle C&={180^\circ }-{95^\circ }\\\angle C&={85^\circ }\\\end{aligned}\end{lgathered}

∠A+∠B+∠C

42

∘

+53

∘

+∠C

∠C

∠C

=180

∘

=180

∘

=180

∘

−95

∘

=85

∘

In triangle RMQ the sum of all angle is {180^ \circ }180

∘

.

\begin{lgathered}\begin{aligned}\angle R+\angle M+\angle Q&=180^{\circ}\\42^{\circ}+\angle M+85^{\circ}&=180^{\circ}\\\angle M&=180^{\circ}-127^{\circ}\\\angle M&=53^{\circ}\end{aligned}\end{lgathered}

∠R+∠M+∠Q

42

∘

+∠M+85

∘

∠M

∠M

=180

∘

=180

∘

=180

∘

−127

∘

=53

∘

Consider the triangle ABC and triangle RMQ.

\angle A=\angle R={42^\circ }∠A=∠R=42

∘

Side AB = RM

\angle B=\angle M∠B=∠M

Therefore, the triangle ABC is congruent to triangle RMQ.

The triangles are congruent by either Angle Side Angle (ASA) or Angle Angle Side (AAS).

Learn more:

1. Learn more about inverse of the function link.

2. Learn more about equation of circle link.

3. Learn more about range and domain of the function link

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Triangle

Keywords: congruent, angles, triangle, ASA, angle side angle, congruent sides, acute angle, side, corresponding angles, congruent triangle.

true

step-by-step explanation: