Quiz Over Properties Of Parallelograms
Quiz over properties of parallelograms
- 1.
Which statement is true:
- A.
All quadrilaterals are rectangles
- B.
All rectangles are quadrilaterals
- C.
All rectangles are squares
- D.
All quadrilaterals are squares
Correct Answer
B. All rectangles are quadrilateralsExplanation
The statement "All rectangles are quadrilaterals" is true because a rectangle is a type of quadrilateral that has four sides and four angles. A quadrilateral is a polygon with four sides. Since a rectangle satisfies the definition of a quadrilateral, it can be concluded that all rectangles are quadrilaterals.Rate this question:
-
- 2.
Identify the quadrilateral which has one pair of parallel sides.
- A.
Kite
- B.
Trapezoid
- C.
Rectangle
- D.
Rhombus
Correct Answer
B. TrapezoidExplanation
A trapezoid is a quadrilateral that has one pair of parallel sides. This means that two sides of the trapezoid are parallel while the other two sides are not. Therefore, the correct answer is trapezoid. A kite has two pairs of consecutive sides that are equal in length, a rectangle has four right angles and opposite sides that are equal in length, and a rhombus has four sides of equal length.Rate this question:
-
- 3.
If a quadrilateral is a parallelogram, then its consecutive angles are ?
- A.
Complementary
- B.
Congruent
- C.
Supplementary
- D.
Equal
Correct Answer
C. SupplementaryExplanation
If a quadrilateral is a parallelogram, then its consecutive angles are supplementary. This is because in a parallelogram, opposite sides are parallel and opposite angles are congruent. Since consecutive angles are the ones that share a side, they are also opposite angles. Therefore, they are congruent and their measures add up to 180 degrees, making them supplementary.Rate this question:
-
- 4.
Which of these descriptions would NOT guarantee that the figure was a square?
- A.
A parallelogram with perpendicular diagonals
- B.
A quadrilateral with all right angles and all sides congruent
- C.
Both a rectangle and a rhombus
- D.
A quadrilateral with all sides and all angles congruent
Correct Answer
A. A parallelogram with perpendicular diagonalsExplanation
A parallelogram with perpendicular diagonals does not guarantee that the figure is a square because a rectangle can also have perpendicular diagonals. Therefore, this description can apply to both squares and rectangles, making it not a guarantee of a square.Rate this question:
-
- 5.
Which of these descriptions would NOT guarantee that a figure was a parallelogram?
- A.
A quadrilateral with consecutive angles supplementary
- B.
A quadrilateral with the diagonals bisecting each other
- C.
A quadrilateral with two opposite sides congruent
- D.
A quadrilateral with one pair of opposite sides both parallel and congruent
Correct Answer
C. A quadrilateral with two opposite sides congruentExplanation
A quadrilateral with two opposite sides congruent does not guarantee that the figure is a parallelogram because a rhombus also has two opposite sides congruent, but it is not a parallelogram. A parallelogram requires that both pairs of opposite sides are congruent.Rate this question:
-
- 6.
Isosceles trapezoid ABCD has legs AB and CD and base BC. If AB = 3y - 9, BC =8y - 2 and CD = 7y - 10, find the value of y.
Correct Answer
.25
1/4Explanation
The given trapezoid is isosceles, which means that the lengths of the legs AB and CD are equal. Therefore, we can set up an equation: 3y - 9 = 7y - 10. Solving this equation, we get y = 1/4 or 0.25. Therefore, the value of y is 0.25 or 1/4.Rate this question:
- 7.
Parallelogram JKLM (pt O is diagonal intersection), angle KLO = 80, angle MLO = 40, find the measure of angle KJM
Correct Answer
120Explanation
In a parallelogram, opposite angles are equal. Since angle KLO is 80 degrees and angle MLO is 40 degrees, angle KJM must also be 80 degrees in order for the opposite angles to be equal. However, since the sum of the angles in a triangle is 180 degrees, angle KJM must be 180 - 80 = 100 degrees. Therefore, the measure of angle KJM is 100 degrees, not 120 degrees.Rate this question:
- 8.
The four properties of the diagonals of squares are
- A.
Congruent to each other, congruent to the sides, bisect both sets of angles, bisect each other
- B.
Bisect each other, bisect one set of angles, are congruent to each other, are perpendicular to each other
- C.
Are congruent to each other, bisect both sets of angles, are perpendicular to each other, are twice the length of the sides
- D.
Are perpendicular to each other, bisect each other, bisect both sets of angles, are congruent to each other
Correct Answer
D. Are perpendicular to each other, bisect each other, bisect both sets of angles, are congruent to each otherExplanation
The answer states that the properties of the diagonals of squares are that they are perpendicular to each other, bisect each other, bisect both sets of angles, and are congruent to each other. This means that the diagonals of a square intersect at a right angle, divide each other into equal segments, divide the angles of the square into equal parts, and have the same length. These properties are unique to squares and help define their geometric characteristics.Rate this question:
-
- 9.
Rhombus MATH, angle HMA = 100, find the measures of angles MTH and MAT
Correct Answer
50 and 80Explanation
In a rhombus, opposite angles are equal. Since angle HMA is given as 100 degrees, angle MTH is also 100 degrees. Additionally, the sum of the angles in a rhombus is always 360 degrees. Since angle HMA is 100 degrees, the sum of angles MAT and MTH must be 360 - 100 = 260 degrees. Therefore, angle MAT is 260 - 100 = 160 degrees. Thus, the measures of angles MTH and MAT are 100 degrees and 160 degrees respectively.Rate this question:
- 10.
LMNP is a rectangle. Find the value of x and the length of each diagonal. LN = 5x - 8 and MP = 2x + 1
Correct Answer
3, 9.9Explanation
In a rectangle, the diagonals are equal in length. So, we have:
LN = MP
Substituting the given expressions for LN and MP, we get:
5x - 8 = 2x + 1
Solving this equation for x, we get:
5x - 2x = 8 + 1
3x = 9
x = 9 / 3 = 3
Now, substituting x = 3 into the expressions for LN and MP, we get:
LN = 5(3) - 8 = 7
MP = 2(3) + 1 = 7
So, the length of each side of the rectangle is 7 units.
The length of the diagonal (D) of a rectangle can be found using the Pythagorean theorem:
D = sqrt(LN^2 + MP^2)
Since LN = MP = 7, we get:
D = sqrt(7^2 + 7^2) = sqrt(98) ≈ 9.9 units
So, the length of each diagonal of the rectangle is approximately 9.9 units.Rate this question:
Quiz Review Timeline +
Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.
-
Current Version
-
Feb 21, 2024Quiz Edited by
ProProfs Editorial Team -
Jan 06, 2010Quiz Created by
Mgarwood
Back to top