Answer:
A) Yes
Explanation:
Congruent triangles are triangles that have the same size and shape. This means that all three corresponding sides and all three corresponding angles are equal.
There are four different congruence criteria that can be used to prove that two triangles are congruent:
- Side-Side-Side (SSS): If all three corresponding sides of two triangles are equal, then the triangles are congruent.
- Side-Angle-Side (SAS): If two corresponding sides and the included angle of two triangles are equal, then the triangles are congruent.
- Angle-Side-Angle (ASA): If two corresponding angles and the included side of two triangles are equal, then the triangles are congruent.
- Angle-Angle-Side (AAS): If two corresponding angles and a non-included side of two triangles are equal, then the triangles are congruent.
In this case:
In the left side triangle respective angle alongside the length 3 is 63° and 72°.
In the right side triangle the respective angle alongside the length 3 is 63° and (180°-45°-63°=72°).
Note: Sum of interior angle of a triangle is equal to 180°. We can find the remaining angle by subtracting two given angles by 180°.
Since the angles value is same.
So, Triangle is congruent to each other by ASA axiom.
Therefore, answer is:
Yes, two triangles are congruent to each other