High school geometry test questions on properties of parallelograms

📚 Quick Study Guide

• 📐 Definition: A parallelogram is a quadrilateral with two pairs of parallel sides.
• 👯 Opposite Sides: Opposite sides of a parallelogram are congruent (equal in length).
• ↔️ Opposite Angles: Opposite angles of a parallelogram are congruent.
• adjacent Consecutive Angles: Consecutive angles of a parallelogram are supplementary (add up to $180^{\circ}$).
• ✂️ Diagonals: The diagonals of a parallelogram bisect each other.
• 📏 Area: The area of a parallelogram is given by the formula $A = b \cdot h$, where $b$ is the base and $h$ is the height.
• ➕ Perimeter: The perimeter of a parallelogram is given by the formula $P = 2(a + b)$, where $a$ and $b$ are the lengths of the sides.

Practice Quiz

1. In parallelogram ABCD, if angle A is $70^{\circ}$, what is the measure of angle C?
   1. $110^{\circ}$
   2. $70^{\circ}$
   3. $90^{\circ}$
   4. $20^{\circ}$
2. If the length of side AB in parallelogram ABCD is 10 cm, what is the length of side CD?
   1. 5 cm
   2. 10 cm
   3. 20 cm
   4. Cannot be determined
3. In parallelogram PQRS, diagonals PR and QS intersect at point T. If PT = 5 cm, what is the length of PR?
   1. 2.5 cm
   2. 5 cm
   3. 10 cm
   4. 15 cm
4. In parallelogram WXYZ, if angle W is $(2x + 10)^{\circ}$ and angle X is $(3x - 30)^{\circ}$, what is the value of x?
   1. 20
   2. 40
   3. 180
   4. 50
5. The area of a parallelogram is 48 $cm^2$ and its base is 8 cm. What is its height?
   1. 4 cm
   2. 6 cm
   3. 8 cm
   4. 12 cm
6. The perimeter of a parallelogram is 30 cm. If one side is 7 cm, what is the length of the adjacent side?
   1. 7 cm
   2. 8 cm
   3. 15 cm
   4. 23 cm
7. Which of the following statements is NOT always true for a parallelogram?
   1. Opposite sides are parallel.
   2. Opposite angles are congruent.
   3. Diagonals are congruent.
   4. Diagonals bisect each other.