Video Transcript
Find the measure of angle
𝐷𝐴𝐵.
When we’re given questions like
this, it’s always good to start with what we’re given. We have triangle 𝐴𝐵𝐶. In this triangle, line segment 𝐴𝐶
is equal in length to line segment 𝐴𝐵. We know the measure of angle 𝐴𝐷𝐵
equals 90 degrees, and we know that the measure of angle 𝐶𝐴𝐷 equals 25
degrees. We want to know the measure of
angle 𝐷𝐴𝐵. That’s this angle. To do that, we take the information
we were given and draw some conclusions. Because line segment 𝐴𝐶 is equal
to line segment 𝐴𝐵 and because the measure of angle 𝐴𝐷𝐵 is 90 degrees, we can
say that line segment 𝐴𝐷 is a perpendicular bisector.
We based that on the converse of
the perpendicular bisector theorem, which tells us that if a point is equidistant
from the ends of two line segments — for us, that would be the line segments 𝐴𝐶
and 𝐴𝐵 that are equal — then the point 𝐴 must fall along the perpendicular
bisector. Because line segment 𝐴𝐷 is a
perpendicular bisector, we can say that line segment 𝐶𝐷 is equal in length to line
segment 𝐵𝐷. We know that this perpendicular
bisector creates two smaller triangles. And we can say that the smaller
triangle 𝐴𝐷𝐶 must be congruent to the smaller triangle 𝐴𝐷𝐵.
We say this based on side-side-side
congruence. Three sides of triangle 𝐴𝐷𝐶 are
equal to the corresponding three sides of triangle 𝐴𝐷𝐵. And since these two triangles are
congruent, we can say that the measure of angle 𝐶𝐴𝐷 will be equal to the measure
of angle 𝐷𝐴𝐵. We’re saying these two angles are
congruent, which makes the measure of angle 𝐷𝐴𝐵 25 degrees.
