Question

given: \\( \angle tsr \\) and \\( \angle qrs \\) are right angles; \\( \angle t \cong \angle q \\) prove: \\( \triangle tsr \cong \triangle qrs \\) step 1: we know that \\( \angle tsr \cong \angle qrs \\) because all right angles are congruent. step 2: we know that \\( \angle t \cong \angle q \\) because it is given. step 3: we know that \\( \overline { sr } \cong \overline { rs } \\) because of the reflexive property. step 4: \\( \triangle tsr \cong \triangle qrs \\) because of the asa congruence theorem. of the aas congruence theorem. of the third angle theorem. all right triangles are congruent.

Explanation:

• ASA (Angle - Side - Angle): Two angles and the included side.
• AAS (Angle - Angle - Side): Two angles and a non - included side.
• In \(\triangle TSR\) and \(\triangle QRS\), we have \(\angle TSR=\angle QRS = 90^{\circ}\) (right angles), \(\angle T=\angle Q\) (given), and \(\overline{SR}=\overline{RS}\) (common side, non - included side for the two given angles).
• The third angle theorem is about the relationship of angles in a triangle when two angles are known. And not all right - triangles are congruent.

Answer:

of the AAS congruence theorem.