High School

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In quadrilateral PQRS, it is given that [tex]PQ = PS[/tex] and [tex]RQ = RS[/tex]. Prove that [tex]\angle PQR = \angle PSR[/tex].

Option 1:
Demonstrate the equality of [tex]\angle PQR[/tex] and [tex]\angle PSR[/tex] in quadrilateral PQRS.

Option 2:
Show that in quadrilateral PQRS, [tex]\angle PQR[/tex] is congruent to [tex]\angle PSR[/tex].

Option 3:
Prove the angle equality: [tex]\angle PQR[/tex] equals [tex]\angle PSR[/tex] in quadrilateral PQRS.

Option 4:
Establish the relationship: [tex]\angle PQR[/tex] is identical to [tex]\angle PSR[/tex] in quadrilateral PQRS.

Answer :

Final answer:

To prove that angle PQR is equal to angle PSR in quadrilateral PQRS, we can use the property of isosceles trapezoids and the congruence of corresponding angles in congruent triangles.

Explanation:

To prove that angle PQR is equal to angle PSR in quadrilateral PQRS, we can use the property of isosceles trapezoids. Since PQ=PS and RQ=RS, we can consider triangle PQS and triangle RQS. Since PQ=PS and RQ=RS, the two triangles are congruent by the Side-Side-Side (SSS) congruence criterion. Therefore, the corresponding angles in congruent triangles are equal, and we can conclude that angle PQR is equal to angle PSR.

Learn more about Congruent triangles here:

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