which sides in triangle pqr are congruent?
select the correct answer.
$\overline{pq}$ and $\overline{pr}$
$\overline{pr}$ and $\overline{qr}$
$\overline{pq}$ and $\overline{qr}$
$\overline{qr}$, $\overline{pq}$ and $\overline{pr}$

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Triangle Angle Sum Theorem" ], "new_concepts": [ "Converse of Isosceles Triangle Theorem" ], "current_concepts": [ "Triangle Angle Sum Theorem", "Converse of Isosceles Triangle Theorem" ] } ## Find the missing angle measure Using the *Triangle Angle Sum Theorem* knowledge point $$ \begin{aligned} m\angle R &= 180^\circ - (m\angle P + m\angle Q) \ m\angle R &= 180^\circ - (65^\circ + 50^\circ) \ m\angle R &= 180^\circ - 115^\circ \ m\angle R &= 65^\circ \end{aligned} $$ ## Identify the congruent sides Since $m\angle P = 65^\circ$ and $m\angle R = 65^\circ$, the triangle has two congruent angles. By the Converse of the Isosceles Triangle Theorem, the sides opposite these congruent angles must also be congruent. - The side opposite $\angle P$ is $\overline{QR}$. - The side opposite $\angle R$ is $\overline{PQ}$. Therefore, the congruent sides are $\overline{PQ}$ and $\overline{QR}$.

$\overline{PQ}$ and $\overline{PR}$

$\overline{PR}$ and $\overline{QR}$

$\overline{PQ}$ and $\overline{QR}$

$\overline{QR}$, $\overline{PQ}$ and $\overline{PR}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Converse of Isosceles Triangle Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Find the missing angle measure

Identify the congruent sides

Answer: