Question

When Carolyn drew the diagonals of parallelogram QRST, four triangles were formed as shown.

Answer 1

The correct answer is A) Only triangle SOR, because QOT and SOR have the same angles therefore in this parallelogram the two triangles are congruent.

Answer 2

Answer: A)  only triangle SOR

Step-by-step explanation:

Since,  In parallelogram QRST,

When we take two traingles QOT and ROS,

$\angle OQT\cong \angle OSR$ ( Because QR is parallel to TS and QS is the common transversal)

$QT\cong RS$ ( by the property of parallelogram)

$\angle OTQ\cong \angle ORS$ ( Because QR is parallel to TS and RT is the common transversal)

Therefore by ASA postulate

$\triangle QOT\cong \triangle ROS$,

But, We can not say that triangle QOT is congruent to triangles  SOT and QOR.

Therefore Only Option A) is correct.