Question

1. given: ( ac cong pc ), ( bc cong qc ) prove: ( \triangle abc cong \triangle pqc )

Explanation:

Step1: Vertical Angles

$\angle ACB\cong\angle PCQ$ (Vertical angles are congruent)

Step2: SAS Congruence

In $\triangle ABC$ and $\triangle PQC$:

• $AC\cong PC$ (Given)
• $\angle ACB\cong\angle PCQ$ (From Step 1)
• $BC\cong QC$ (Given)

By the Side - Angle - Side (SAS) congruence criterion, $\triangle ABC\cong\triangle PQC$

Answer:

$\triangle ABC\cong\triangle PQC$ by the SAS (Side - Angle - Side) congruence criterion.