Question

△twg≅△qha
which other congruence statements are true?
select each correct answer.
□△wtg≅△hqa
□△wgt≅△haq
□△gwt≅△aqh
□△tgw≅△qah

Explanation:

Step1: Recall congruent - triangle naming rules

When two triangles are congruent, the order of the vertices in the congruence statement matters. Corresponding vertices must be in the same order. Given $\triangle TWG\cong\triangle QHA$, the corresponding vertices are: $T$ corresponds to $Q$, $W$ corresponds to $H$, and $G$ corresponds to $A$.

Step2: Check each option

• For $\triangle WTG\cong\triangle HQA$: Here, the first - vertex $W$ corresponds to $H$, $T$ corresponds to $Q$, and $G$ corresponds to $A$. But the order is wrong as per the given $\triangle TWG\cong\triangle QHA$.
• For $\triangle WGT\cong\triangle HAQ$: The first - vertex $W$ corresponds to $H$, $G$ corresponds to $A$, and $T$ corresponds to $Q$. The order of vertices matches the corresponding vertices of the given congruent triangles.
• For $\triangle GWT\cong\triangle AQH$: The first - vertex $G$ corresponds to $A$, $W$ corresponds to $Q$, and $T$ corresponds to $H$. The order is wrong.
• For $\triangle TGW\cong\triangle QAH$: The first - vertex $T$ corresponds to $Q$, $G$ corresponds to $A$, and $W$ corresponds to $H$. The order of vertices matches the corresponding vertices of the given congruent triangles.

Answer:

• $\triangle WGT\cong\triangle HAQ$
• $\triangle TGW\cong\triangle QAH$