Parallelograms Special Quadrilaterals Test – Geometry Math (Printable PDF)

Question 1 Parallelogram sides (2 points)

In parallelogram PQRS, PQ = 7x − 9 and SR = 4x + 12. Find x (1 point) and PQ (1 point).

Question 2 Parallelogram angles (3 points)

In parallelogram PQRS, m∠P = (5x + 8)° and m∠Q = (7x + 16)°.

1. Find x. (1 point)
2. Find m∠P and m∠Q. (1 point)
3. Find m∠R and m∠S. (1 point)

Question 3 Diagonal pieces (2 points)

The diagonals of parallelogram ABCD meet at E. AE = 2x + 5 and EC = 4x − 11. Find x and the length of AC.

Question 4 Test for a parallelogram (3 points)

Decide whether each quadrilateral must be a parallelogram. Answer yes or no and give a reason.

1. The diagonals bisect each other. (1 point)
2. One pair of opposite sides is parallel and the other pair is congruent. (1 point)
3. Both pairs of opposite angles are congruent. (1 point)

Question 5 Rhombus measures (3 points)

Rhombus ABCD has side length 17. Diagonal AC is 16 units long and the diagonals meet at E.

1. Find BE. (1 point)
2. Find the length of diagonal BD. (1 point)
3. Find the area of the rhombus. (1 point)

Question 6 Prove diagonals give a parallelogram (3 points)

Given: In quadrilateral ABCD, the diagonals meet at E, with AE ≅ CE and BE ≅ DE. Prove: AB ≅ CD and AB ∥ CD.

Question 7 Trapezoids (2 points)

A trapezoid has bases of 14 and 26. (1 point) Find its midsegment. If the trapezoid is isosceles with a base angle of 65°, find the measure of the angle next to it along a leg. (1 point)

Question 8 Kite angles (2 points)

Kite ABCD has AB = AD and CB = CD. m∠B = 112° and m∠A = 76°. Find m∠D (1 point) and m∠C (1 point).