Question

Given angle adb \cong angle cdb ∠ adb ≅ ∠ cdb prove triangle adb △ adb is a right triangle

a) Triangle adb △ adb is a right triangle
b) Triangle adb △ adb is an acute triangle
c) Triangle adb △ adb is an obtuse triangle
d) Triangle adb △ adb cannot be determined

Answer 1

To prove that triangle adb △ adb is a right triangle, we need to show that one of the angles in the triangle is 90 degrees. Given that angle adb ≈ angle cdb (∠ adb ≈ ∠ cdb), we can conclude that triangle adb △ adb is isosceles.

Step-by-step explanation:

To prove that triangle adb △ adb is a right triangle, we need to show that one of the angles in the triangle is 90 degrees.

Given that angle adb ≈ angle cdb (∠ adb ≈ ∠ cdb), we can conclude that triangle adb △ adb is isosceles. In an isosceles triangle, the angles opposite the congruent sides are also congruent.

Since angle adb ≈ angle cdb, the angles opposite the congruent sides are congruent as well. This means that angle adb and angle cdb are equal in measure. Since the sum of the angles in a triangle is 180 degrees, and angle adb + angle cdb = 180 degrees, we can conclude that angle adb and angle cdb are each 90 degrees.