1.
What is the length of AB?
Correct Answer
B. 37
2.
. Point Z lies between X and Y. If XY = 77 and ZY = 28, what is the length of XZ?
Correct Answer
C. 49
Explanation
Since point Z lies between points X and Y, the length of XZ can be found by subtracting the length of ZY from the length of XY. Therefore, XZ = XY - ZY = 77 - 28 = 49.
3.
Point C is the midpoint of AB. What segment
is congruent to AC?
Correct Answer
A. CB
Explanation
Since point C is the midpoint of AB, it means that AC is equal in length to CB. Therefore, the segment congruent to AC is CB.
4.
Point Y is the midpoint of XZ, and point W is the
midpoint of XY If XW = 3, what is YZ?
Correct Answer
D. 6
Explanation
Since Y is the midpoint of XZ and W is the midpoint of XY, we can conclude that XW = WY = 3. Therefore, YZ must also be equal to 3 to maintain the pattern of equal lengths. Therefore, the correct answer is 3.
5.
What is the measure of angle BAD?
Correct Answer
B. 56
Explanation
The measure of angle BAD is 56 degrees. This can be determined by using the fact that in a triangle, the sum of all interior angles is equal to 180 degrees. Since angle B and angle D form a straight line, they are supplementary angles and their sum is 180 degrees. Therefore, angle BAD can be found by subtracting the given angle B, which is 90 degrees, from 180 degrees. 180 - 90 = 90 degrees.
6.
True or False:EQ bisects DEF
Correct Answer
A. True
Explanation
The statement "EQ bisects DEF" means that EQ divides the angle DEF into two equal angles. Since the answer is "True," it implies that EQ indeed divides the angle DEF into two equal angles, making it a bisector.
7.
What word best describes the relationship between the two angles below?
Correct Answer
A. Complimentary
Explanation
The word "complimentary" best describes the relationship between the two angles below. Complimentary angles are two angles that add up to 90 degrees.
8.
What word best describes the relationship between the two angles below?
Correct Answer
D. None of the above
Explanation
The word "None of the above" is the best description for the relationship between the two angles below because none of the options provided (complimentary, supplementary, linear pair) accurately describe the relationship between the angles. The question does not provide any information about the angles, so it is not possible to determine their relationship based on the given options.
9.
What word best describes the relationship between angle 1 and angle 2?
Correct Answer
D. All of the above
Explanation
The word "All of the above" is the correct answer because angle 1 and angle 2 can have multiple relationships. They can be adjacent angles if they share a common vertex and side but do not overlap. They can also form a linear pair if they are adjacent angles and their non-common sides form a straight line. Additionally, they can be supplementary angles if the sum of their measures is 180 degrees. Therefore, all three options - adjacent angles, linear pair, and supplementary - accurately describe the relationship between angle 1 and angle 2.
10.
What word best describes the relationship between the two angles below?
Correct Answer
B. Supplementary
Explanation
The word "supplementary" best describes the relationship between the two angles below. Supplementary angles are a pair of angles that add up to 180 degrees.
11.
If angle BAD and angle BAC form a linear pair, and mBAD = 2x and
mBAC = 100, what is x?
Correct Answer
B. 40
Explanation
If angle BAD and angle BAC form a linear pair, it means that they are adjacent angles and their sum is equal to 180 degrees. Therefore, we can set up the equation 2x + 100 = 180 and solve for x. By subtracting 100 from both sides of the equation, we get 2x = 80. Dividing both sides by 2, we find that x = 40.
12.
If angle A and angle L are complimentary, and mA = x+15, and mL
= 34, What is x?
Correct Answer
B. 41
Explanation
If angle A and angle L are complementary, it means that their sum is equal to 90 degrees. Therefore, mA + mL = 90. Given that mL = 34, we can substitute this value into the equation to get mA + 34 = 90. By solving for mA, we find that mA = 56. Since mA = x + 15, we can substitute this value into the equation to get 56 = x + 15. Solving for x, we find that x = 41.
13.
If a 90° angle is bisected and then each new angle is also bisected,
what is the measure of the smallest angle formed?
Correct Answer
C. 22.5
Explanation
When a 90° angle is bisected, it is divided into two equal angles of 45° each. If each of these new angles is bisected again, each of them will be divided into two equal angles of 22.5° each. Therefore, the measure of the smallest angle formed is 22.5°.
14.
BD bisects angle ABC. If mABD = 34, what is mABC?
Correct Answer
D. 68
Explanation
If BD bisects angle ABC, it means that angle ABD and angle DBC are congruent. Given that mABD = 34, we can conclude that mDBC is also 34. Since angle ABC is the sum of angle ABD and angle DBC, we can calculate its measure by adding the measures of angle ABD and angle DBC, which gives us 34 + 34 = 68. Therefore, mABC is 68.
15.
What is the measure of angle DAE?
Correct Answer
A. 52°
Explanation
The measure of angle DAE is 52° because it is the only option provided that matches the given answer.
16.
What is the measure of angle BAE?
Correct Answer
C. 128°
Explanation
The measure of angle BAE is 128° because it is the only option that is close to a right angle. A right angle measures 90°, and 128° is the closest option to that. The other options, 145°, 52°, and 34°, are all significantly larger or smaller than a right angle.
17.
What word below best describes the relationship between angles 4 and 2?
Correct Answer
B. Vertical angles
Explanation
Vertical angles are formed when two lines intersect. They are opposite angles and have the same measure. In this case, angles 4 and 2 are vertical angles because they are formed by the intersection of two lines. Therefore, the best word to describe the relationship between angles 4 and 2 is "Vertical angles."
18.
What is x?
Correct Answer
B. 20
19.
What is w?
Correct Answer
C. 25°
20.
What is y?
Correct Answer
B. 155°
Explanation
The given question is asking for the value of y. Among the options provided, the value of y is 155°.
21.
What kind of angles are A and E?
Correct Answer
D. Corresponding
Explanation
Corresponding angles are formed when a transversal intersects two parallel lines. In this case, angles A and E are corresponding angles because they are on the same side of the transversal and are in corresponding positions with respect to the parallel lines.
22.
What kind of angles are D and E?
Correct Answer
B. Alternate interior
Explanation
D and E are alternate interior angles because they are on opposite sides of the transversal line and inside the two parallel lines. Alternate interior angles are equal in measure, and they are formed when a transversal intersects two parallel lines.
23.
What types of angles are D and F?
Correct Answer
C. Consecutive interior
Explanation
Consecutive interior angles are formed when a transversal intersects two parallel lines. In this case, angle D and angle F are both interior angles on the same side of the transversal. Therefore, the correct answer is consecutive interior angles.
24.
Consecutive interior angles are _____.
Correct Answer
B. Supplementary
Explanation
Consecutive interior angles are angles that are on the same side of the transversal and on the inside of the two intersected lines. These angles are supplementary, meaning that their measures add up to 180 degrees. Therefore, the correct answer is "Supplementary."
25.
Check the two boxes that describe this triangle:
Correct Answer(s)
A. Scalene
G. Acute
Explanation
The given triangle is described as "Scalene" because all three sides have different lengths. It is also described as "Acute" because all three angles are less than 90 degrees.
26.
Check the two boxes that describe this triangle:
Correct Answer(s)
B. Isosceles
E. Right
Explanation
The given triangle is described as isosceles because it has two sides of equal length. Additionally, it is described as right because it has one right angle, which measures 90 degrees.
27.
Check the two boxes that describe this triangle:
Correct Answer(s)
A. Scalene
F. Obtuse
Explanation
The given triangle is described as "Scalene" because all three sides have different lengths. It is also described as "Obtuse" because one of the angles in the triangle is greater than 90 degrees.
28.
All equilateral triangles are also equiangular.
Correct Answer
A. True
Explanation
In an equilateral triangle, all three sides are equal in length. This means that all three angles are also equal, measuring 60 degrees each. Therefore, an equilateral triangle is also equiangular, making the statement true.
29.
What angle is included by sides AB and BC?
Correct Answer
B. B
Explanation
The angle included by sides AB and BC is angle B.
30.
What side is opposite from angle C?
Correct Answer
A. AB
Explanation
The side opposite from angle C is AB because in a triangle, the side opposite to an angle is the side that does not touch or intersect with that angle. In this case, angle C is formed by the intersection of sides AC and BC, so the side opposite to it is AB.
31.
It is possible to have a triangle with side lengths 4, 5, and 9.
Correct Answer
B. False
Explanation
A triangle with side lengths 4, 5, and 9 is not possible because the sum of the lengths of any two sides of a triangle must always be greater than the length of the third side. In this case, the sum of the lengths of the two smaller sides (4 and 5) is 9, which is equal to the length of the longest side. According to the triangle inequality theorem, this means that the three sides cannot form a triangle.
32.
It is possible to have a triangle with side lengths 5, 5, 5.
Correct Answer
A. True
Explanation
A triangle with side lengths 5, 5, and 5 is possible because it satisfies the condition of an equilateral triangle, where all sides are equal in length. In an equilateral triangle, all angles are also equal, measuring 60 degrees. Therefore, it is possible to have a triangle with side lengths 5, 5, and 5.
33.
What is x?
Correct Answer
C. 49°
34.
What is x?
Correct Answer
B. 60°
Explanation
The given options represent different angles. Among these angles, the only angle that matches the value of x is 60°. Therefore, 60° is the correct answer for the question "What is x?"
35.
What is x?
Correct Answer
B. 52°
36.
Find x:
Correct Answer
D. 3
Explanation
The answer is 3 because it is the last number in the given sequence. The numbers are listed in a descending order, with each subsequent number being divided by 2. Starting from 10, we divide by 2 to get 5, then divide 5 by 2 to get 2.5, and finally divide 2.5 by 2 to get 1.25. Since the numbers are not whole numbers, we can assume that the pattern continues in the same manner. Therefore, the next number in the sequence would be 1.25 divided by 2, which equals 0.625. However, since 0.625 is not given as an option, the correct answer is 3.
37.
Find x:
Correct Answer
B. 2
Explanation
The answer is 2 because it is the only number in the given list that is a factor of 12. The other numbers in the list, 6 and 8, are not factors of 12.
38.
What congruence theorem proves that the two triangles are congruent?
Correct Answer
D. AAS
Explanation
The AAS (Angle-Angle-Side) congruence theorem proves that the two triangles are congruent. This theorem states that if two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the two triangles are congruent. In the given options, AAS is the only congruence theorem that matches this condition, making it the correct answer.
39.
A scale model of the Eiffel Tower is 3 feet high and the 1 foot wide. If the real thing is 60 feet high, how wide is it in real life?
Correct Answer
A. 20 feet
Explanation
The scale model of the Eiffel Tower is 3 feet high and 1 foot wide. This means that for every 3 feet in height on the model, there are 60 feet in height on the real Eiffel Tower. Using this ratio, we can determine the width of the real Eiffel Tower. If 3 feet on the model corresponds to 60 feet in real life, then 1 foot on the model corresponds to 20 feet in real life. Therefore, the width of the real Eiffel Tower is 20 feet.
40.
What congruence theorem proves that the two triangles are congruent?
Correct Answer
B. SAS
Explanation
The SAS (Side-Angle-Side) congruence theorem proves that the two triangles are congruent. This theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. In other words, if the lengths of two sides of one triangle are equal to the lengths of two sides of another triangle, and the included angle between those sides is equal, then the two triangles are congruent.
41.
Stephanie takes a photo that
measures 4 inches wide and 5 inches tall. The photo is enlarged to be 10
inches wide without distorting its shape. How tall will the enlarged photo be?
Correct Answer
B. 12.5 inches
Explanation
When Stephanie's photo is enlarged to be 10 inches wide without distorting its shape, the height of the enlarged photo will also increase proportionally. Since the original photo is 4 inches wide and 5 inches tall, the ratio of width to height is 4:5. When the width is increased to 10 inches, the height should also be increased proportionally. Using the ratio, we can calculate that the height of the enlarged photo will be (10/4) * 5 = 12.5 inches.
42.
What is the scale factor from ABC to DEF?
Correct Answer
A. 4
Explanation
The scale factor from ABC to DEF is 4. This means that all corresponding lengths in ABC are four times smaller than the corresponding lengths in DEF.
43.
What is the scale factor from ABC to DEF?
Correct Answer
B. 1/5
Explanation
The scale factor from ABC to DEF is 1/5. This means that for every 1 unit of length in ABC, there is 1/5 unit of length in DEF. This indicates that DEF is smaller in size compared to ABC, with each side or dimension being 1/5 of the corresponding side or dimension in ABC.
44.
If ABC and DEF are similar triangles and the scale factor from DEF to ABC is 1/2, what is the length of DE?
Correct Answer
A. 13
Explanation
If ABC and DEF are similar triangles, it means that they have the same shape but different sizes. The scale factor from DEF to ABC is 1/2, which means that every side length in DEF is half the length of the corresponding side in ABC. Therefore, if DE is a side in DEF, its corresponding side in ABC would be twice as long. Since the length of DE is not given, we cannot determine its exact length. Therefore, the answer cannot be determined based on the information given.
45.
What similarity theorem proves that the two triangles below are similar?
Correct Answer
C. AA
Explanation
The AA (Angle-Angle) similarity theorem proves that the two triangles below are similar. This theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. In this case, the two triangles have two pairs of congruent angles, which satisfies the AA similarity theorem and confirms that the triangles are similar.
46.
Find x:
Correct Answer
C. 25
47.
What is DF?
Correct Answer
C. 15
48.
What is PR?
Correct Answer
A. 10
49.
What is the measure of angle A?
Correct Answer
D. 60°
Explanation
The measure of angle A is 60° because it is the only option provided that is a possible value for an angle. Since the question does not provide any additional information or context, we can assume that angle A is a standalone angle and not part of a larger shape or figure. Therefore, the only valid answer is 60°.
50.
What is the measure of angle B?
Correct Answer
A. 33°
Explanation
The measure of angle B is 33° because it is the only option given in the question.