Question

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

Explanation:

Step1: Recall vertical - angle property

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

Step2: Analyze ∠XZR and ∠TZN

∠XZR and ∠TZN are vertical angles formed by the intersection of lines XR and MT. So, ∠XZR≅∠TZN.

Step3: Analyze ∠GNH and ∠KNT

∠GNH and ∠KNT are not vertical angles. ∠GNH and ∠KNH are complementary (since ∠KNH = 90°), and ∠KNT is not related to ∠GNH as vertical - angles. So, ∠GNH≇∠KNT.

Step4: Analyze ∠GQM and ∠NTM

∠GQM and ∠NTM are corresponding angles. When two parallel lines are cut by a transversal, corresponding angles are congruent. But there is no information indicating parallel lines here, and they are not vertical angles. So, ∠GQM≇∠NTM.

Step5: Analyze ∠QTZ and ∠NTM

∠QTZ and ∠NTM are vertical angles formed by the intersection of lines QM and XR. So, ∠QTZ≅∠NTM.

Step6: Analyze ∠KNH and ∠ZNG

∠KNH = 90° and ∠ZNG is an acute angle. So, ∠KNH≇∠ZNG.

Answer:

∠XZR≅∠TZN, ∠QTZ≅∠NTM