Question Video: Finding the Measure of an Angle in a Triangle given the Corresponding Angle’s Measure in a Congruent Triangle | Nagwa Question Video: Finding the Measure of an Angle in a Triangle given the Corresponding Angle’s Measure in a Congruent Triangle | Nagwa

# Question Video: Finding the Measure of an Angle in a Triangle given the Corresponding Angleβs Measure in a Congruent Triangle Mathematics • First Year of Preparatory School

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In the following figure, find πβ π½πΎπΏ.

02:13

### Video Transcript

In the following figure, find the measure of angle π½πΎπΏ.

Letβs begin by looking at the diagram and identifying that angle π½πΎπΏ is part of the triangle π½πΎπΏ, which is at the top part of this figure. There is also another triangle ππΎπΏ below this in the figure. We can observe that both these triangles are in fact right triangles, since the two angles of πΏπ½πΎ and πΏππΎ both have measures of 90 degrees.

Next, we can see from the markings on the triangles that the line segment π½πΏ is congruent to the line segment ππΏ. We might wonder at this point if the triangles π½πΎπΏ and ππΎπΏ are congruent to each other. As both of these triangles are right triangles, we can consider if the right angle-hypotenuse-side, or RHS, criterion would apply.

The line segment πΎπΏ is the hypotenuse in both triangles. And since it is common to both triangles, then we know that it is congruent in each. So we have demonstrated that there is a pair of right angles. The hypotenuse in each triangle is congruent. And there is another pair of congruent sides. We have therefore proved that triangle π½πΎπΏ is congruent to triangle ππΎπΏ by the RHS congruence criterion.

We note that angles π½πΎπΏ and ππΎπΏ are corresponding. So the measure of angle π½πΎπΏ is the same as the measure of ππΎπΏ. They are both 34 degrees. So, by first proving that the triangles were congruent, we have found the unknown angle measure of π½πΎπΏ as 34 degrees.

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