Question

Question

For the picture below: XY = 8, CD = 8. <X = 87 degrees, <Z=57 degrees, <D = 36 degrees and <B = 57 degrees.

Part 1. Explain how you can use the Triangle Sum theorem and the AAS congruency theorem to prove the two triangles congruent. (2pts)

Part 2. Write a correct congruency statement. You may use the = instead of the congruency symbol. (2pts)

write both answers like a lazy student, the ansewer should be correct but given in the simplest form

Answer 1

Part 1: So, we have two triangles to compare. We can use the Triangle Sum theorem, which says the angles in a triangle add up to 180 degrees. For one triangle, angles <X, <Y, and <Z add up to 180, and we know two angles (<X and <Z), so we can find <Y. For the other triangle, we already know angle <D, <B, and the third angle will be similar since the rest will add up to 180 as well.

Then, we can use the AAS (Angle-Angle-Side) congruency theorem because we have two angles and one side (XY = CD) for both triangles. This means the triangles are congruent.

Part 2: Triangle XYZ = Triangle DBC (or XYZ = DBC)