Question

7 finish the triangle proof by dragging the correct reasons to their box. there will be two extra unused reasons! given: mp bisects ∠nml and ∠npl prove: ∠mlp ≅ ∠mnp

Explanation:

Step1: Identify the given information

The first statement "MP bisects ∠NML and ∠NPL" is given, so the reason is "Given".

Step2: Use the definition of angle bisector

When a ray bisects an angle, it divides the angle into two equal parts. So, for ∠LMP = ∠NMP (statement 2) and ∠LPM = ∠NPM (statement 3), the reason is "Definition of Bisect".

Step3: Apply the reflexive property

For MP = MP (statement 4), by the reflexive property of equality (a quantity is equal to itself), the reason is "Reflexive Property".

Step4: Use the ASA (Angle - Side - Angle) congruence criterion

In triangles \( \triangle MLP\) and \( \triangle MNP\), we have two angles (\( \angle LMP=\angle NMP\) and \( \angle LPM = \angle NPM\)) and the included side (\(MP = MP\)). So, \( \triangle MLP\cong\triangle MNP\) by ASA. But we want to prove \( \angle MLP\cong\angle MNP\). After proving \( \triangle MLP\cong\triangle MNP\) (using ASA for the triangles), we use CPCTC (Corresponding Parts of Congruent Triangles are Congruent) to get \( \angle MLP\cong\angle MNP\).

Answer:

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