Question

proof complete the paragraph proof.
given: ∠acb ≅ ∠qsr, (overline{ac} cong overline{qs}), ∠cab and ∠sqr are right angles.
prove: ( \triangle acb cong \triangle qsr )
proof: we are given that ∠cab and ∠sqr are right angles. because all right angles are select choice congruent, ∠cab ≅ ∠sqr. we are also given that ∠acb select choice to ∠qsr and that (overline{ac}) select choice to (overline{qs}). from this, we know that ( \triangle acb cong \triangle qsr ) by the select choice congruence postulate.

Explanation:

Step1: Analyze Right Angles

All right angles are congruent, so $\angle CAB \cong \angle SQR$ (since both are right angles).

Step2: Identify Given Congruences

We are given $\angle ACB \cong \angle QSR$ and $\overline{AC} \cong \overline{QS}$.

Step3: Apply AAS Congruence

For triangles $\triangle ACB$ and $\triangle QSR$, we have:

• $\angle CAB \cong \angle SQR$ (right angles, congruent)
• $\angle ACB \cong \angle QSR$ (given)
• $\overline{AC} \cong \overline{QS}$ (given)

This matches the Angle - Angle - Side (AAS) congruence postulate, which states that if two angles and a non - included side of one triangle are congruent to the corresponding two angles and non - included side of another triangle, then the triangles are congruent.

Answer:

The congruence postulate is AAS (Angle - Angle - Side). So the first "Select Choice" (about right angles congruence) is "congruent", the second "Select Choice" (about $\angle ACB$ and $\angle QSR$) is "congruent", the third "Select Choice" (about $\overline{AC}$ and $\overline{QS}$) is "congruent", and the last "Select Choice" (congruence postulate) is "AAS (Angle - Angle - Side)".