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 Angle’s Measure in a Congruent Triangle Mathematics • First Year of Preparatory School

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In the following figure, find 𝑚∠𝐽𝐾𝐿.

02:13

Video Transcript

In the following figure, find the measure of angle 𝐽𝐾𝐿.

Let’s begin by looking at the diagram and identifying that angle 𝐽𝐾𝐿 is part of the triangle 𝐽𝐾𝐿, which is at the top part of this figure. There is also another triangle 𝑀𝐾𝐿 below this in the figure. We can observe that both these triangles are in fact right triangles, since the two angles of 𝐿𝐽𝐾 and 𝐿𝑀𝐾 both have measures of 90 degrees.

Next, we can see from the markings on the triangles that the line segment 𝐽𝐿 is congruent to the line segment 𝑀𝐿. We might wonder at this point if the triangles 𝐽𝐾𝐿 and 𝑀𝐾𝐿 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 𝐾𝐿 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 𝐽𝐾𝐿 is congruent to triangle 𝑀𝐾𝐿 by the RHS congruence criterion.

We note that angles 𝐽𝐾𝐿 and 𝑀𝐾𝐿 are corresponding. So the measure of angle 𝐽𝐾𝐿 is the same as the measure of 𝑀𝐾𝐿. They are both 34 degrees. So, by first proving that the triangles were congruent, we have found the unknown angle measure of 𝐽𝐾𝐿 as 34 degrees.

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