Question

cw: triangle congruence theorems
if not congruent, write none in both slots.
these triangles can be proven congruent by □. δnop ≅ δ□

Explanation:

Step1: Identify the common side

In the figure, \(NP\) is a common side for \(\triangle NOP\) and \(\triangle NQP\). So \(NP = NP\) (reflexive property of equality).

Step2: Analyze the angles

We are given that \(\angle ONP=\angle QNP\) and \(\angle OPN=\angle QPN\)

Step3: Apply the ASA (Angle - Side - Angle) congruence theorem

Since we have two angles and the included side equal (\(\angle ONP=\angle QNP\), \(NP = NP\), \(\angle OPN=\angle QPN\)), by the ASA (Angle - Side - Angle) congruence theorem, \(\triangle NOP\cong\triangle NQP\)

Answer:

These triangles can be proven congruent by \(ASA\). \(\triangle NOP\cong\triangle NQP\)