Question

1. prove △egf≅△bac. 6. prove △abc≅△rpq. 7. prove △mln≅△prq. 8. prove △prq≅△trs. 9. determine if each equation is a correct step in the process of solving 2(7 + 5x)-3x=-35 for x. select yes or no for each equation. 14 + 10x - 6x=-35 14 + 10x - 3x=-35

Explanation:

5.

Step1: Identify equal - angle and - side pairs

From the figure, we can see that $\angle E=\angle B$, $EF = BC$ (marked), $\angle F=\angle C$.

Step2: Apply congruence criterion

By the Angle - Side - Angle (ASA) congruence criterion, since two angles and the included side of $\triangle EGF$ are equal to two angles and the included side of $\triangle BAC$, we have $\triangle EGF\cong\triangle BAC$.

Step1: Identify equal - angle and - side pairs

We observe that $\angle A=\angle R$, $AC = RQ$ (marked), $\angle C=\angle Q$.

Step2: Apply congruence criterion

By the ASA congruence criterion, $\triangle ABC\cong\triangle RPQ$ because two angles and the included side of $\triangle ABC$ are equal to two angles and the included side of $\triangle RPQ$.

Step1: Identify equal - side pairs

We have $ML = PR$, $LN=RQ$, $MN = PQ$ (marked).

Step2: Apply congruence criterion

By the Side - Side - Side (SSS) congruence criterion, since all three sides of $\triangle MLN$ are equal to all three sides of $\triangle PRQ$, we have $\triangle MLN\cong\triangle PRQ$.

Answer:

$\triangle EGF\cong\triangle BAC$ by ASA

6.