Question

knows that $overline{pt}congoverline{qt}$ by the diagonals of a parallelogram. is floyd correct? explain your reasoning. 11. reason write a two - column - proof. given: $abcd$ and $cfgh$ are parallelograms. prove: $angle acongangle g$. statements reasons

Explanation:

Step1: Recall parallelogram properties

In parallelogram \(ABCD\), \(\angle A=\angle C\) (opposite - angles of a parallelogram are congruent).

Step2: Recall properties of another parallelogram

In parallelogram \(CFGH\), \(\angle C = \angle G\) (opposite - angles of a parallelogram are congruent).

Step3: Use the transitive property

Since \(\angle A=\angle C\) and \(\angle C=\angle G\), then \(\angle A\cong\angle G\) by the transitive property of congruence.

Statements	Reasons
2. \(\angle A=\angle C\)	Opposite angles of a parallelogram are congruent
3. \(CFGH\) is a parallelogram	Given
4. \(\angle C=\angle G\)	Opposite angles of a parallelogram are congruent
5. \(\angle A\cong\angle G\)	Transitive property of congruence

Answer:

The two - column proof is shown above to prove \(\angle A\cong\angle G\).