Question Video: Determining the Congruency of Triangles | Nagwa Question Video: Determining the Congruency of Triangles | Nagwa

# Question Video: Determining the Congruency of Triangles Mathematics • First Year of Preparatory School

## Join Nagwa Classes

True or False: In the given figure, if πβ π΅ = πβ πΆ and the line segment π΄π· is a bisector of β π΄, then triangle π΄π΅π· is congruent to triangle π΄π·πΆ.

02:16

### Video Transcript

True or False: In the given figure, if the measure of angle π΅ is equal to the measure of angle πΆ and the line segment between π΄ and π· is a bisector of angle π΄, then triangle π΄π΅π· is congruent to triangle π΄π·πΆ.

In this question, we are given a geometric figure and asked to determine if two triangles in the figure are congruent, which means that they would have corresponding sides of the same length and corresponding angles of the same measure. We can do this by considering the congruency criteria for triangles. Letβs begin by adding the given information onto the sketch.

First, we are told that the measure of angles π΅ and πΆ are equal. Second, we are told that line segment π΄π· bisects the angle at π΄. This means that it splits the angle into two angles of equal measure as shown.

There are a few different ways to consider the congruency of the two triangles. One way is to note that triangle π΄π΅πΆ is isosceles since it has two angles of equal measure. We can then recall that the isosceles triangle theorem tells us that the sides opposite the congruent angles in an isosceles triangle have the same length. So, π΄π΅ is equal to π΄πΆ as shown.

We have now shown that triangles π΄π΅π· and π΄πΆπ· have two angles of equal measure and the included side of these corresponding angles have the same length. This is enough to prove that the two triangles are congruent using the angle-side-angle congruence criterion. Hence, the answer is true.

## Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

• Interactive Sessions
• Chat & Messaging
• Realistic Exam Questions