Question

Hi, I need help asap.
Use the diagram and given information to answer the questions and prove the statement.

Given: ∠X ≅ ∠Z
("XY" ) ̅ ≅ ("ZY" ) ̅
Prove: ("AZ" ) ̅ ≅ ("BX" ) ̅


a)Re-draw the diagram of the overlapping triangles so that the two triangles are separated.

b) What additional information would be necessary to prove that the two triangles, XBY and ZAY, are congruent? What congruency theorem would be applied?

c)Prove ("AZ" ) ̅ ≅ ("BX" ) ̅ using a flow chart proof.

Answer 1

part a) draw two triangles, translating one of them to the right.

part b) Consider triangles ΔYXB and ΔYZA. In these triangles:

• ∠Y is common, then ∠XYB≅∠ZYA (additional information that is needed);
• ∠YXB≅∠YZA (given);
• XY≅ZY (given).

Therefore, these two triangles have two congruent angles adjacent to congruent sides. By the ASA Postulate, ΔYXB≅ΔYZA.

ASA Postulate: If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the triangles are congruent.

part c) flow chart proof:

$\triangle YXB\cong \triangle YZA\Rightarrow$

• XY≅ZY (given);
• XB≅ZA (implies);
• YB≅YA (implies).

Answer 2

Answer:

ASA-Angle-Side-Angle

Step-by-step explanation:

Spilt the Triangles

∠X≅∠Z---ANGLE

XY≅ZY---SIDE

∠Y is a right angle---ANGLE

ASA---Angle-Side-Angle