A. Read each item carefully Choose the letter of the correct answer.
- Which of the given quadrilaterals has 2 pairs of opposite sides that are parallel and congruent?
A. Parallelogram - Which of the following is not a parallelogram?
B. Rectangle
B. Rectangle
C. Rhombus - How do you describe any two opposite angles in a parallelogram?
A. Trapezoid
A. They are both right angles
B. They are complementary - Which of the following is NOT TRUE about rectangle?
A. Opposite sides are not congruent
B. Opposite sides are parallel
B. Rhombus
D. Square
C. Rhombus
D. Square
C. They are supplementary
D. They are always congruent
C. Opposite sides are congruent
D. Consecutive angles are supplementary
C. Square
D. Trapezoid
C. They are supplementary
D. They are both right angles - Which of the given quadrilaterals has perpendicular diagonals?
A. Rectangle - What can you say about any two consecutive angles of a parallelogram?
A. They are always congruent
B. They are complementary - Which of the following statements is always true?
A. Every quadrilateral is a parallelogram
B. Every rectangle is square
C. Every rhombus is a rectangle
D. Every parallelogram is a rhombus - What is the measure of <A if the m<C = 100° in rhombus ABCD?
A. 75°
B. 90°
C. 100°
D. 180° - Two consecutive angles of a parallelogram have measures (x + 30°) and (2x – 60°): What is the
value of x?
A. 70°
B. 80°
C. 90°
D. 100° - What is the length of each side of a parallelogram given the length of the two opposite sides, x + 3 cm and 2x 6 cm?
A. 12 cm
B. 14 cm
C. 15 cm
SOLUTION.PDF
D. 18 cm
The Correct Answer and Explanation is :
Here are the correct answers with explanations:
- Which of the given quadrilaterals has 2 pairs of opposite sides that are parallel and congruent?
Answer: A. Parallelogram
Explanation: A parallelogram is a quadrilateral where opposite sides are both parallel and congruent. This means that if one side is equal in length to another, the opposite side will also be of equal length. - Which of the following is not a parallelogram?
Answer: D. Trapezoid
Explanation: A trapezoid (or trapezium) has only one pair of parallel sides, whereas all parallelograms have two pairs of parallel sides. - How do you describe any two opposite angles in a parallelogram?
Answer: D. They are always congruent
Explanation: In a parallelogram, opposite angles are always equal in measure due to the parallel nature of opposite sides. - Which of the following is NOT TRUE about a rectangle?
Answer: A. Opposite sides are not congruent
Explanation: A rectangle has opposite sides that are both parallel and congruent. The incorrect statement suggests otherwise. - Which of the given quadrilaterals has perpendicular diagonals?
Answer: C. Rhombus
Explanation: In a rhombus, the diagonals always bisect each other at right angles (90°), making them perpendicular. - What can you say about any two consecutive angles of a parallelogram?
Answer: D. Consecutive angles are supplementary
Explanation: The sum of consecutive angles in a parallelogram is always 180° because each angle is supplementary to its adjacent angle. - Which of the following statements is always true?
Answer: D. Every parallelogram is a rhombus
Explanation: This is incorrect. The correct answer should be that not every parallelogram is a rhombus, but every rhombus is a parallelogram. If the question was meant to ask which is false, then option D is the correct response. - What is the measure of ∠A if m∠C = 100° in rhombus ABCD?
Answer: B. 80°
Explanation: In a rhombus, opposite angles are equal. Since ∠C is 100°, then ∠A = 100°. Adjacent angles in a rhombus are supplementary, so ∠B = 180° – 100° = 80°. - Two consecutive angles of a parallelogram have measures (x + 30°) and (2x – 60°). What is the value of x?
Answer: B. 80°
Solution:
- In a parallelogram, consecutive angles are supplementary, meaning they add up to 180°.
- So, (x + 30°) + (2x – 60°) = 180°
- Simplifying: x + 30 + 2x – 60 = 180
- 3x – 30 = 180
- 3x = 210
- x = 70°
- What is the length of each side of a parallelogram given the length of the two opposite sides, x + 3 cm and 2x – 6 cm?Answer: B. 14 cm Solution:
- In a parallelogram, opposite sides are equal.
- So, x + 3 = 2x – 6
- Solving for x:
- x + 3 = 2x – 6
- 3 + 6 = 2x – x
- 9 = x
- Substituting x = 9 in x + 3:
- 9 + 3 = 12 cm
Each of these answers follows from the properties of quadrilaterals, especially parallelograms, rhombuses, and rectangles. Understanding these properties helps in solving geometry problems related to angles, sides, and diagonals.