Video Transcript
In the given figure, if πΏπππ is
a rectangle, π΄π equals π΅π, and the measure of angle πππΆ equals 50 degrees,
find the measure of angle πππΆ.
Since πΏπππ is a rectangle, all
of its internal angles are right angles. This means that the complementary
angles at πΏ and π are also right angles. Therefore, π΄ππ and π΅πΏπ are a
pair of right triangles with congruent hypotenuses. Since πΏπππ is a rectangle,
segments πΏπ and ππ are also congruent. But π΄ππ and π΅πΏπ are right
triangles. So the Pythagorean theorem now
fixes the length of the third side in each triangle.
We can conclude that triangles
π΄ππ and π΅πΏπ are congruent. It follows immediately that angles
πππΆ and πππΆ are congruent. That is, angle πππΆ has measure
50 degrees.