1.
Which of the following statements is true?
Correct Answer
D. The diagonals of an isosceles trapezoid bisect each other.
Explanation
The diagonals of an isosceles trapezoid bisect each other because an isosceles trapezoid has two pairs of congruent angles and the diagonals connect the opposite vertices. Since the opposite angles are congruent, the diagonals divide each other into equal halves, resulting in the diagonals bisecting each other.
2.
How do you describe any two opposite angles in a parallelogram?
Correct Answer
A. They are always congruent.
Explanation
In a parallelogram, opposite angles are formed when two lines intersect. These opposite angles are always congruent, meaning they have the same measure. This is a property of parallelograms, and it holds true for all parallelograms regardless of their size or shape. Therefore, the correct answer is that any two opposite angles in a parallelogram are always congruent.
3.
The diagonals of an isosceles trapezoid are represented by 4x – 47 and 2x + 31. What is the value of x?
Correct Answer
B. 39
Explanation
The diagonals of an isosceles trapezoid are congruent, meaning they have equal lengths. Therefore, we can set the two expressions representing the diagonals equal to each other and solve for x.
4x - 47 = 2x + 31
Simplifying the equation, we get:
2x = 78
Dividing both sides by 2, we find:
x = 39
Therefore, the value of x is 39.
4.
A cross section of a water trough is in the shape of a trapezoid with bases measuring 2 m and 6 m. What is the length of the median of the trapezoid?
Correct Answer
B. 4 m
Explanation
The median of a trapezoid is the line segment that connects the midpoints of the two bases. In this case, the bases measure 2 m and 6 m. The midpoint of the 2 m base is 1 m, and the midpoint of the 6 m base is 3 m. Therefore, the length of the median is the difference between these two midpoints, which is 3 m - 1 m = 2 m.
5.
What are the measures of the sides of parallelogram SOFT in meters?
Correct Answer
B. {5 m , 6 m}
Explanation
The measures of the sides of parallelogram SOFT are 5 meters and 6 meters.
6.
What can you say about any two consecutive angles in a parallelogram?
Correct Answer
B. They are always supplementary.
Explanation
In a parallelogram, opposite angles are congruent. Since opposite angles are formed by intersecting lines, they are also supplementary, meaning that the sum of their measures is always 180 degrees. Therefore, any two consecutive angles in a parallelogram will always be supplementary to each other.
7.
Find the length of the longer diagonal in parallelogram FAST.
Correct Answer
C. 46
8.
Find the value of y in the figure below.
Correct Answer
B. 30
9.
In the rhombus RHOM, what is the measure of <ROH?
Correct Answer
C. 55°
Explanation
The measure of angle ROH in a rhombus is always equal to the measure of angle ROM, where M is the midpoint of OH. In a rhombus, all angles are equal, so if the measure of angle ROM is 55°, then the measure of angle ROH is also 55°.
10.
Which of the following statements is true?
Correct Answer
B. Every rectangle is a square.
Explanation
Every rectangle is a square because a square is a special type of rectangle where all four sides are equal in length. A rectangle, on the other hand, can have sides of different lengths. Therefore, every square can be classified as a rectangle, but not every rectangle can be classified as a square.
11.
In the rectangle KAYE, YO = 18 cm. Find the length of diagonal AE.
Correct Answer
D. 36 cm
Explanation
In a rectangle, the diagonals are equal in length. Since YO is given as 18 cm and YO is a diagonal, the length of AE, which is also a diagonal, will be the same. Therefore, the length of diagonal AE is 36 cm.
12.
Which of the following statements could be false?
Correct Answer
D. The diagonals of a rhombus are congruent but not perpendicular to each other.
Explanation
The statement "The diagonals of a rhombus are congruent but not perpendicular to each other" could be false because in a rhombus, the diagonals are always congruent and they are always perpendicular to each other.
13.
Which of the following quadrilaterals has diagonals that do not bisect each other?
Correct Answer
D. None of the above
Explanation
A square has diagonals that bisect each other, dividing the square into four congruent right triangles. A rhombus also has diagonals that bisect each other, dividing the rhombus into four congruent triangles. A trapezoid, on the other hand, does not have diagonals that bisect each other. The diagonals of a trapezoid intersect each other, but they do not divide the trapezoid into congruent parts. Therefore, the correct answer is "None of the above" as none of the given quadrilaterals have diagonals that do not bisect each other.
14.
Which of the following conditions is not sufficient to prove that a quadrilateral is a parallelogram?
Correct Answer
C. Two angles are complementary.
Explanation
If two angles are complementary in a quadrilateral, it does not necessarily mean that the quadrilateral is a parallelogram. A parallelogram has opposite angles that are congruent, but this condition is not mentioned in the answer choice. Therefore, two angles being complementary is not sufficient to prove that a quadrilateral is a parallelogram.
15.
What condition will make parallelogram WXYZ a rectangle?
Correct Answer
C. < X is a right angle.
Explanation
If angle X is a right angle, it means that it measures 90 degrees. In a parallelogram, opposite angles are congruent, so if one angle is 90 degrees, then all four angles in the parallelogram are 90 degrees. This makes the parallelogram a rectangle, as rectangles have four right angles. Therefore, if angle X is a right angle, parallelogram WXYZ will be a rectangle.
16.
The perimeter of a parallelogram is 34 cm. If a diagonal is 1 cm less than its length and 8 cm more than its width, what are the dimensions of this parallelogram?
Correct Answer
A. 4 cm x 13 cm
Explanation
The perimeter of a parallelogram is the sum of all its sides. Let's assume the length of the parallelogram is L and the width is W. The diagonal is given as L-1, and it is also given that the diagonal is 8 cm more than the width, so we can write the equation L-1 = W+8. The perimeter is given as 34 cm, so we can write the equation 2L + 2W = 34. Solving these two equations simultaneously, we get L = 13 and W = 4. Therefore, the dimensions of the parallelogram are 4 cm x 13 cm.
17.
What is the measurement of < 2 in rhombus HOME?
Correct Answer
C. 105°
Explanation
In a rhombus, opposite angles are equal. Since angle 2 is opposite to angle 4, and angle 4 is given as 105°, angle 2 must also be 105°.
18.
Which of the following statements is/are true about isosceles trapezoid?
Correct Answer
C. Both a and b
Explanation
An isosceles trapezoid is a trapezoid with two sides that are congruent. This means that the diagonals, which connect the opposite vertices, will also be congruent. Additionally, the median of an isosceles trapezoid, which is a line segment connecting the midpoints of the non-parallel sides, will be parallel to the bases. Therefore, both statements a and b are true about isosceles trapezoids.
19.
Two consecutive angles of a parallelogram have measures (x + 30)° and [2(x – 30)]°. What is the measure of the smaller angle?
Correct Answer
B. 80°
Explanation
The measure of the smaller angle in a parallelogram can be found by subtracting the larger angle from 180°. In this case, the larger angle is [2(x – 30)]° and the smaller angle is (x + 30)°. Therefore, the measure of the smaller angle is [180 - 2(x – 30)]°, which simplifies to [180 - 2x + 60]° and further simplifies to [240 - 2x]°. To find the value of x, we set [240 - 2x]° equal to 80° and solve for x. This gives us x = 80, which means the measure of the smaller angle is 80°.