Question

a diagram is shown. which of the following statements are true? select all that apply.
□ ∠xzr≅∠tzn
□ ∠gnh≅∠knt
□ ∠gqm≅∠ntm
□ ∠qtz≅∠ntm
□ ∠knh≅∠zng
□ ∠gnh≅∠znt

Explanation:

Step1: Recall vertical - angle property

Vertical angles are congruent. Vertical angles are formed when two lines intersect.

Step2: Analyze $\angle XZR$ and $\angle TZN$

$\angle XZR$ and $\angle TZN$ are vertical angles formed by the intersection of lines $QR$ and $MH$. So, $\angle XZR\cong\angle TZN$.

Step3: Analyze $\angle GNH$ and $\angle KNT$

$\angle GNH$ and $\angle KNT$ are not vertical angles. $\angle GNH$ is an angle formed by line $GH$ and $NG$, and $\angle KNT$ is formed by lines $MH$ and $NK$. They are not congruent.

Step4: Analyze $\angle GQM$ and $\angle NTM$

$\angle GQM$ and $\angle NTM$ are corresponding angles (assuming some parallel - line relationship which is not given, but we can also consider the non - congruence based on the intersection of non - parallel lines here). They are not vertical angles and not congruent in general.

Step5: Analyze $\angle QTZ$ and $\angle NTM$

$\angle QTZ$ and $\angle NTM$ are vertical angles formed by the intersection of lines $QR$ and $MG$. So, $\angle QTZ\cong\angle NTM$.

Step6: Analyze $\angle KNH$ and $\angle ZNG$

$\angle KNH$ and $\angle ZNG$ are vertical angles formed by the intersection of lines $MH$ and $GH$. So, $\angle KNH\cong\angle ZNG$.

Step7: Analyze $\angle GNH$ and $\angle ZNT$

$\angle GNH$ and $\angle ZNT$ are not vertical angles. They are not congruent.

Answer:

$\angle XZR\cong\angle TZN$, $\angle QTZ\cong\angle NTM$, $\angle KNH\cong\angle ZNG$