Question

problem 23
clear
given: abcd and afgh
are parallelograms.
prove: ∠g ≅ ∠c

Explanation:

Step1: Properties of parallelograms

In parallelogram \(ABCD\), \(\angle A\cong\angle C\) (opposite angles of a parallelogram are congruent). In parallelogram \(AFGH\), \(\angle A\cong\angle G\) (opposite angles of a parallelogram are congruent).

Step2: Transitive property

Since \(\angle A\cong\angle C\) and \(\angle A\cong\angle G\), by the transitive property of congruence (\(if\ a = b\ and\ a = c,\ then\ b = c\)), we have \(\angle G\cong\angle C\).

Answer:

1. \(ABCD\) and \(AFGH\) are parallelograms.
2. \(\angle A\cong\angle C\) (opposite angles of parallelogram \(ABCD\) are congruent); \(\angle A\cong\angle G\) (opposite angles of parallelogram \(AFGH\) are congruent).
3. \(\angle G\cong\angle C\) (transitive property of congruence).