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Math  /  Geometry

QuestionWhich rule explains why these triangles are congruent? (A) SSS (B) ASA (c) SAS (D) Not enough information to prove congruence.

Studdy Solution

STEP 1

1. We are given two triangles, △MPJ \triangle MPJ and △QPN \triangle QPN .
2. The angles at M M and Q Q , J J and N N , and the angle at P P are marked as congruent.

STEP 2

1. Identify the congruent angles in both triangles.
2. Determine the rule that applies based on the given information.

STEP 3

Identify the congruent angles in both triangles:
- ∠M≅∠Q\angle M \cong \angle Q - ∠J≅∠N\angle J \cong \angle N - ∠P≅∠P\angle P \cong \angle P (common angle)

STEP 4

Determine the rule that applies based on the given information:
Since we have two pairs of congruent angles and the included angle is also congruent, the rule that applies is ASA (Angle-Side-Angle).
The rule that explains why these triangles are congruent is:
ASA \boxed{\text{ASA}}

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