Question

hw 5: proving triangles congruent: sss & sas
state whether the triangles could be proven congruent, if possible, by sss or sas. then, write a congruency statement.
4.
the triangles ▼ congruent by ▼
△▼▼▼ ≅ △▼▼▼

Explanation:

Step1: Identify Congruent Sides

From the diagram, \( MN = QP \) (marked with one tick), \( MQ = NP \) (marked with two ticks), and \( NQ \) is a common side to both \( \triangle MNQ \) and \( \triangle PQN \). So all three sides of \( \triangle MNQ \) are equal to the corresponding sides of \( \triangle PQN \).

Step2: Determine Congruence Criterion

Since all three corresponding sides are equal, the SSS (Side - Side - Side) congruence criterion applies. So the triangles are congruent by SSS.

Step3: Write Congruency Statement

The congruent triangles are \( \triangle MNQ \) and \( \triangle PQN \), so \( \triangle MNQ \cong \triangle PQN \). Also, the first blank for "The triangles" should be "are" as the triangles are congruent.

Answer:

The triangles \(\boldsymbol{\text{are}}\) congruent by \(\boldsymbol{\text{SSS}}\)

\(\triangle \boldsymbol{M}\boldsymbol{N}\boldsymbol{Q} \cong \triangle \boldsymbol{P}\boldsymbol{Q}\boldsymbol{N}\)