Question

The figure below shows a kite labeled PQRS.
Write a 2-column, paragraph, or flow-chart proof to show that angle PQR is congruent to angle PSR.

Answer 1

@Mertsj
@jim_thompson5910
@sugargurl

Answer 2

In triangle PQR and Triangle PSR

PQ = PS ( adjacent sides of a kite are equal)
QR = RS (adjacent sides of a kite are equal)
RS = common side

therefore triangles PQR and PSR are congruent by Side, Side Side test.

Then angle PQR = Angle PSR corresponding angles in congruent triangles are equal.

proven as required.

Answer 3

THANK YOU!!

Answer 4

SSS (Side-Side-Side):

Two triangles are considered congruent (geometrically equal) if we can prove that all three corresponding sides are equal (congruent).

AAAS (Angle-Angle-Angle-Side):
Two triangles are considered congruent (geometrically equal) if we can prove that all three corresponding angles are equal and that one corresponding side is equal (congruent). Because of the nature of triangles (the sum of the angles of a triangle equal 180), we actually only have to prove AA (Angle-Angle) to prove AAA (Angle-Angle-Angle); knowing this, we can rewrite this condition as simply AAS (Angle-Angle-Side).

SAS (Side-Angle-Side):
Two triangles are considered congruent (geometrically equal) if we can provide that two corresponding sides and the included corresponding angle are equal.

HL (Hypotenuse-Leg)
This particular condition only works with two right triangles. If the corresponding hypotenuse (that is, the side opposite the right angle) and a corresponding leg (non-hypotenuse side) are equal, then we've proved that the two right triangles are congruent (geometrically equal).

If we were to prove, for two right triangles, that both corresponding legs (non-hypotenuse sides) are equal, we would have proved that the two triangles are congruent (geometrically equal) by SAS (Side-Angle-Side) since the included corresponding angle would have been equal by definition of "right triangle."