given angle amd and zdm are right angles

given: segment AM and ZD are congruent

prove: angle a is congruent to z (CPCTC)

I know that reflexive prop is needed and all right angles are congruent, also sas

Please help with 3 statements_

To prove that angle A is congruent to angle Z using the CPCTC (Corresponding Parts of Congruent Triangles are Congruent) postulate, we need to show that triangle AMD is congruent to triangle ZDM.

Given:
1. Angle AMD and angle ZDM are right angles. (This means that angle AMD and angle ZDM both measure 90 degrees.)
2. Segment AM and segment ZD are congruent.

To prove: Angle A is congruent to angle Z.

Proof:

Statement 1: Triangle AMD is congruent to triangle ZDM. (To prove that angles A and Z are congruent, we need to prove that the entire triangles are congruent.)

Reason for Statement 1: We will use the SAS (Side-Angle-Side) criterion to prove that the two triangles are congruent.
- SAS states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Statement 2: Segment AD is congruent to segment ZD. (This is a result of the reflexive property.)

Reason for Statement 2: Reflexive property states that any segment is congruent to itself.

Statement 3: Angle A is congruent to angle Z. (This follows from the congruence of the entire triangles.)

Reason for Statement 3: By the CPCTC postulate, corresponding parts of congruent triangles are congruent. Since triangle AMD is congruent to triangle ZDM (Statement 1), and in triangle AMD angle A is congruent to angle A (reflexive property), it follows that angle A is congruent to angle Z.

Therefore, based on the given information and the steps of the proof, we can conclude that angle A is congruent to angle Z.