Video Transcript
In the given figure, triangle
𝐴𝐵𝐶 is congruent to triangle 𝐿𝑀𝑁. Determine the measure of angle
𝑁.
In this problem, we have two
triangles: 𝐴𝐵𝐶 on the left and 𝐿𝑀𝑁 on the right. We are given the information that
triangle 𝐴𝐵𝐶 is congruent to triangle 𝐿𝑀𝑁. Congruent triangles have all three
pairs of corresponding sides congruent and all three pairs of corresponding angles
congruent.
When we are given a congruency
relationship like this, we can use the order of letters to establish which sides and
vertices are corresponding. So we can take the first vertex of
each triangle in the relationship to establish that vertex 𝐴 in triangle 𝐴𝐵𝐶
corresponds to vertex 𝐿 in triangle 𝐿𝑀𝑁. Vertex 𝐵 corresponds to vertex 𝑀,
and vertex 𝐶 corresponds to vertex 𝑁. And because of the congruency of
the triangles, each pair of corresponding angles at each vertex will be
congruent.
We are asked to determine the
measure of angle 𝑁. We’ve already noted that angles 𝐶
and 𝑁 are corresponding, so their measures are equal. They will therefore both be 48
degrees. And so by using the congruency of
the triangles, we have found that the measure of angle 𝑁 is 48 degrees.
Although not required here, we can
note that the measure of angle 𝑀 is equal to the measure of angle 𝐵, so it is 33
degrees. And the measure of angle 𝐿 is
equal to the measure of angle 𝐴. They are both 99 degrees.
