Question

ABCD is a quadrilateral. Another quadrilateral PQRS is congruent (same size and

shape to ABCD). P and S measure 80° which of the statements could be true:

1. PQ =AB

2. Q is right angle.

3. All sides of PQRS are of same length.

4. The area of PQRS is less than the area of ABCD. ​

Answer 1

Given  : ABCD is a quadrilateral  

Another quadrilateral PQRS is congruent to ABCD

∠P and ∠S measures 80°

To Find : which of the statements could be true:

1. PQ =AB

2 ∠Q is right angle

3 All sides of PQRS are of same length.

4 :  The area of PQRS is less than the area of ABCD.

Solution:

Corresponding part of congruent figures are equal in measures

Hence

∠A = ∠P = 80°

∠B =∠Q

∠C = ∠R

∠D =∠S =  80°

AB = PQ

BC = QR

CD = RS

AD = PS

Hence 1 ) PQ =AB  must be true as corresponding sides

From the figure ABCD is a trapezium with AD || BC

Hence ∠A + ∠B = 180°  and ∠C + ∠D = 180°

∠A = ∠D = 80°

=> ∠B = 100°  ,  ∠C = 100°

∠B =∠Q => ∠Q  = 100°

Hence ∠Q is right angle can not be true

All sides of PQRS are of same length can bot be true

as AD ≠ BC  hence PS ≠ QR

Area of congruent figures are equal

Hence  The area of PQRS is less than the area of ABCD. ​ can not be True

Hence Correct answer is option 1) PQ = AB

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