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Q.

According to the ____ congruence, it is shown that ΔPOS≅ΔQOR.

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Detailed Solution

Given,
∠POS=40°
∠PSO=60°
∠QRO=60°
∠POS=∠QOR=40∘ (Two angles are opposite to each and lie on the same lines are equal)
It is known that the sum of the angles of a triangle is 180°.
Since, ∠SPO =180° - 60° + 40° = 80°
and also ∠OQR=80° (Both are alternate angles)
So, according to the AAA (Angle angle angle) congruence criteria, that is,
∠POS = ∠QOR = 40°
∠SPO = ∠OQR = 80°
∠PSO = ∠QRO = 60°
Now, we can say that the triangle ΔPOS is similar to ΔQOR, that is ΔPOS≅ΔQOR.
Therefore, according to the AAA congruence, it is shown that ΔPOS≅ΔQOR.

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