1.
Name this figure.
Correct Answer
A. Line segment AB
Explanation
The figure is named "line segment AB" because it represents a straight line with two endpoints, A and B. A line segment is a part of a line that is bounded by two distinct points, and in this case, those points are A and B.
2.
Name this figure.
Correct Answer
B. Line CD
Explanation
The figure shown in the question is a line segment, which is a part of a line with two endpoints. In this case, the line segment is named CD, indicating that it starts at point C and ends at point D. Therefore, the correct answer is "line CD."
3.
Name this figure.
Correct Answer
C. Ray EF
Explanation
The figure in question is a ray, specifically ray EF. A ray is a part of a line that has one endpoint and extends infinitely in one direction. In this case, the endpoint is E and it extends in the direction of F.
4.
Name this figure.
Correct Answer
D. Plane GHI
Explanation
The figure is named "plane GHI" because a plane is a flat, two-dimensional surface that extends infinitely in all directions. In the given figure, GHI represents three non-collinear points, which form a plane. A line segment, line, and ray are all one-dimensional objects and do not extend infinitely in all directions like a plane does. Therefore, the correct answer is "plane GHI".
5.
Describe these lines.
Correct Answer
B. Intersecting
Explanation
The lines described in the question are either parallel or intersecting. The word "neither" indicates that the lines are not parallel, so they must be intersecting.
6.
Describe these planes.
Correct Answer
A. Parallel
Explanation
The term "parallel" refers to two or more planes that do not intersect each other. In other words, they never meet or cross paths. Instead, they remain at a constant distance from each other, maintaining the same direction throughout. This can be visualized as two train tracks that run alongside each other without ever converging or diverging. Therefore, the correct answer for this question is "parallel."
7.
Are points J and K collinear?
Correct Answer
A. Yes
8.
Are points L and M coplanar?
Correct Answer
B. No
Explanation
Points L and M are not coplanar because they do not lie on the same plane. Coplanar points are points that lie on the same plane, meaning they can be connected by a straight line without leaving the plane. However, without any additional information or context, it is not possible to determine the exact positions of points L and M and their relationship to each other.
9.
What is the distance between points R and S?* SHOW YOUR WORK *
Correct Answer
C. 5
Explanation
The distance between points R and S is 5.
10.
Line M bisects line segment LN.
What is the length of MN?* SHOW YOUR WORK *
Correct Answer
A. 5
Explanation
Line M bisects line segment LN, which means that it divides LN into two equal parts. Therefore, the length of MN is equal to half the length of LN. Since the length of LN is not given in the question, we cannot determine the exact length of MN. Hence, the correct answer cannot be determined based on the information provided.
11.
Point P is the midpoint of line segment OQ.
What is the length of PQ?* SHOW YOUR WORK *
Correct Answer
B. 10
Explanation
Since point P is the midpoint of line segment OQ, it means that the distance from point O to point P is the same as the distance from point P to point Q. Therefore, the length of PQ is equal to the length of OP, which is 10.
12.
What is the length of RU?* SHOW YOUR WORK *
Correct Answer
C. 9
13.
Classify this angle.
Correct Answer
C. Obtuse
Explanation
The given angle is classified as obtuse because it measures more than 90 degrees but less than 180 degrees.
14.
Classify this angle.
Correct Answer
B. Right
Explanation
The angle is classified as "right" because it measures exactly 90 degrees.
15.
Classify this angle.
Correct Answer
E. Reflex
Explanation
A reflex angle is an angle that measures greater than 180 degrees and less than 360 degrees. It is formed when the two arms of the angle are on opposite sides of the initial arm. In this case, since the question does not provide any information about the angle's measurement or position, we can classify it as a reflex angle based on the given options.
16.
Classify this angle.
Correct Answer
A. Acute
Explanation
An acute angle is an angle that measures less than 90 degrees. In this case, since there is no additional information given about the angle, we can only classify it based on the options provided. The given answer of "acute" indicates that the angle in question measures less than 90 degrees.
17.
Angle GKH and angle HKJ are complementary. The measurement of angle HKJ is 60 degree.
Find the measurement of angle GKH.* SHOW YOUR WORK *
Correct Answer
A. 30
Explanation
Angle GKH and angle HKJ are complementary, which means that the sum of their measures is 90 degrees. We are given that the measure of angle HKJ is 60 degrees. To find the measure of angle GKH, we subtract 60 from 90, which gives us 30 degrees. Therefore, the measurement of angle GKH is 30 degrees.
18.
Angle LOM and angle MON are supplementary.
The measure of angle MON is 80 degrees.
Find the measurement of angle LOM.* SHOW YOUR WORK *
Correct Answer
C. 100
Explanation
Angle LOM and angle MON are supplementary, which means that the sum of their measures is equal to 180 degrees. Given that the measure of angle MON is 80 degrees, we can subtract this value from 180 to find the measure of angle LOM. Therefore, the measurement of angle LOM is 100 degrees.
19.
Name the transversal.
Correct Answer
C. Line CB
Explanation
The transversal in this case is line CB because it intersects two other lines, AB and CD. A transversal is a line that crosses two or more other lines, and in this scenario, line CB fits that criteria.
20.
Describe these lines.
Correct Answer
B. Perpendicular
Explanation
The lines described in the question can be categorized as either parallel, perpendicular, or neither. The correct answer, "Perpendicular," indicates that the lines being described are at right angles to each other.
21.
Find the measurement of angle 1.* SHOW YOUR WORK *
Correct Answer
A. 100
Explanation
To find the measurement of angle 1, we can use the fact that angles in a triangle add up to 180 degrees. Since angle 1 is part of a triangle, we can subtract the given angles (80 and 120) from 180 to find the measurement of angle 1.
180 - 80 - 120 = 100
Therefore, the measurement of angle 1 is 100 degrees.
22.
Find the measurement of angle 3.
Correct Answer
B. 80
Explanation
The measurement of angle 3 is 80 degrees.
23.
Find the measurement of angle 6.
Correct Answer
B. 80
Explanation
Angle 6 can be determined by using the property of supplementary angles. Since angle 1 and angle 6 are vertical angles, they are congruent. Angle 1 measures 100 degrees, so angle 6 also measures 100 degrees. Since angle 6 and angle 5 are supplementary angles, their measures add up to 180 degrees. Therefore, angle 5 measures 80 degrees. Since angle 5 and angle 6 are congruent, angle 6 also measures 80 degrees.
24.
Find the measurement of angle 7.
Correct Answer
B. 80
Explanation
Angle 7 can be found by using the property of supplementary angles. Since angle 7 and angle 3 are adjacent angles on a straight line, they are supplementary, which means they add up to 180 degrees. Therefore, angle 7 must be equal to 180 degrees minus angle 3. Since angle 3 is given as 100 degrees, angle 7 can be calculated as 180 - 100 = 80 degrees.
25.
Find the measurement of angle 8.
Correct Answer
A. 100
Explanation
Angle 8 can be determined by subtracting the measurement of angle 2 (which is 80 degrees) from the measurement of angle 10 (which is 180 degrees). Therefore, angle 8 would measure 100 degrees.
26.
Classify this triangle according to its angles.
Correct Answer
B. Right
Explanation
This triangle is classified as a right triangle because it has one angle that measures exactly 90 degrees.
27.
Classify this triangle according to its angles.
Correct Answer
A. Acute
Explanation
This triangle can be classified as "acute" because all of its angles are less than 90 degrees.
28.
Classify this triangle according to its angles.
Correct Answer
C. Obtuse
Explanation
This triangle is classified as obtuse because it has one angle that is greater than 90 degrees.
29.
Classify this angle according to its sides.
Correct Answer
A. Equilateral
Explanation
This angle can be classified as equilateral because an equilateral angle has all three sides of equal length.
30.
Classify this angle according to its sides.
Correct Answer
C. Scalene
Explanation
The angle in question is classified as scalene because it does not have any sides that are equal in length. In a scalene angle, all three sides have different lengths.
31.
Classify this angle according to its sides.
Correct Answer
B. Isosceles
Explanation
An isosceles angle is a type of angle that has two sides of equal length. In this case, since the angle is classified as isosceles, it means that two sides of the angle are equal in length. This is different from an equilateral angle, where all three sides are equal in length, and a scalene angle, where all three sides are different lengths.
32.
Find the measurement of the interior angle X.(Hint: The interior sum of a triangle is 180 degrees.)* SHOW YOUR WORK *
Correct Answer
A. 40
Explanation
The sum of the interior angles of a triangle is always 180 degrees. Since we know that one of the interior angles of the triangle is 100 degrees, we can subtract that from 180 to find the sum of the other two angles. 180 - 100 = 80. Since the other two angles must add up to 80 degrees, and we know that one of those angles is 40 degrees, we can subtract 40 from 80 to find the measurement of the remaining angle. 80 - 40 = 40 degrees. Therefore, the measurement of interior angle X is 40 degrees.
33.
Find the measurement of the exterior angle X.* SHOW YOUR WORK *
Correct Answer
B. 60
Explanation
To find the measurement of the exterior angle X, we need to use the fact that the sum of the measures of the exterior angles of a polygon is always 360 degrees. Since there is no information given about the polygon in the question, we can assume that it is a regular polygon. In a regular polygon, all exterior angles are congruent. Therefore, we can divide 360 degrees by the number of exterior angles to find the measurement of each exterior angle. In this case, since there are 6 possible choices for the exterior angle X, we divide 360 by 6 to get 60 degrees. Therefore, the measurement of the exterior angle X is 60 degrees.
34.
Find the length of X.(Hint: X is a midsegment.)* SHOW YOUR WORK *
Correct Answer
B. 6
Explanation
The length of X can be found by dividing the length of the longer segment by 2. In this case, the longer segment has a length of 12. So, dividing 12 by 2 gives us 6, which is the length of X.
35.
Are triangles ABC and FDE congruent?
Correct Answer
A. Yes
Explanation
The question is asking whether triangles ABC and FDE are congruent. The answer is "Yes" because congruent triangles have the same shape and size. If triangles ABC and FDE are congruent, it means that their corresponding sides and angles are equal. However, without any additional information or context about the triangles, it is difficult to provide a more specific explanation.
36.
How are these two triangles congruent?
What is the best reason?
Correct Answer
A. Side-Side-Side (SSS)
Explanation
The triangles are congruent because all three sides of one triangle are equal in length to the corresponding sides of the other triangle. This is known as the Side-Side-Side (SSS) congruence criterion.
37.
How are these two triangles congruent?
What is the best reason?
Correct Answer
C. Angle-Side-Angle (ASA)
Explanation
The two triangles are congruent because they have two pairs of corresponding angles that are equal and a pair of corresponding sides that are equal. This satisfies the Angle-Side-Angle (ASA) congruence criterion, which states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.
38.
How are these two triangles congruent?
What is the best reason?
Correct Answer
B. Side-Angle-Side (SAS)
Explanation
The given information states that the two triangles are congruent. The best reason for their congruence is Side-Angle-Side (SAS). This means that the two triangles have two pairs of corresponding sides that are congruent and one pair of corresponding angles that are congruent.
39.
How are these two triangles congruent?
What is the best reason?
Correct Answer
D. Angle-Angle-Side (AAS)
Explanation
The two triangles are congruent because they have two pairs of congruent angles and one pair of congruent sides. This is known as the Angle-Angle-Side (AAS) congruence criterion.
40.
One leg of a right triangle measures 6 in. The other leg measures 8 in. What is the length of the hypotenuse? Hint: Use the Pythagorean theorem: a^2 + b^2 = c^2 * SHOW YOUR WORK *
Correct Answer
C. 10
Explanation
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In this case, we have one leg measuring 6 inches (a) and the other leg measuring 8 inches (b). To find the length of the hypotenuse, we can substitute these values into the formula: 6^2 + 8^2 = c^2. Simplifying this equation gives us 36 + 64 = c^2. Adding the two values together gives us 100 = c^2. Taking the square root of both sides gives us c = 10. Therefore, the length of the hypotenuse is 10 inches.
41.
The hypotenuse of a right triangle measures 5 inches. One leg measures 4 inches. What is the length of the other leg? Hint: Use the Pythagorean theorem: a^2 + b^2 = c^2 * SHOW YOUR WORK *
Correct Answer
C. 3
Explanation
Using the Pythagorean theorem, we can find the length of the other leg. The theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the hypotenuse measures 5 inches and one leg measures 4 inches. Let's call the length of the other leg "x". Applying the theorem, we have 4^2 + x^2 = 5^2. Simplifying this equation, we get 16 + x^2 = 25. Subtracting 16 from both sides, we get x^2 = 9. Taking the square root of both sides, we find that x = 3. Therefore, the length of the other leg is 3 inches.
42.
This is a 45-45-90 special triangle. Find the length of the missing side.
Correct Answer
A. 9
Explanation
This is a 45-45-90 special triangle, which means that the two shorter sides are congruent and the longer side is the hypotenuse. In this case, the given length of one of the shorter sides is 9. Since the two shorter sides are congruent, the length of the missing side is also 9.
43.
This is a 30-60-90 special triangle. Find the length of the missing side. * SHOW YOUR WORK *
Correct Answer
B. 8
Explanation
This is a 30-60-90 special triangle, which means that the angles of the triangle are 30 degrees, 60 degrees, and 90 degrees. In a 30-60-90 triangle, the ratio of the sides is 1:√3:2. Here, the side opposite the 30 degree angle is 4, so the side opposite the 60 degree angle is 4√3. Therefore, the missing side, which is opposite the 90 degree angle, is 8.
44.
Classify this polygon according to the number of its sides.
Correct Answer
A. Pentagon
Explanation
The given correct answer is "Pentagon". A polygon is a closed figure with straight sides. It is classified based on the number of sides it has. A pentagon is a polygon with five sides. Therefore, the given figure can be classified as a pentagon.
45.
Classify this polygon according to the number of its sides.
Correct Answer
C. Octagon
Explanation
The given answer "Octagon" is correct because an octagon is a polygon that has eight sides. It is classified as an octagon based on the number of sides it has.
46.
Find the measurement of an interior angle of this regular polygon. Hint: 180 x (number of sides - 2) / (number of sides)* SHOW YOUR WORK *
Correct Answer
B. 90
Explanation
The formula for finding the measurement of an interior angle of a regular polygon is 180 x (number of sides - 2) / (number of sides). Plugging in the values, we get 180 x (4 - 2) / 4 = 180 x 2 / 4 = 360 / 4 = 90. Therefore, the measurement of an interior angle of this regular polygon is 90 degrees.
47.
Find the measurement of the exterior angle of this regular polygon. Hint: 360 / (number of sides)* SHOW YOUR WORK *
Correct Answer
C. 60
48.
The exterior sum of all polygons is _____.
Correct Answer
B. 360
Explanation
The exterior sum of all polygons is 360. This is because the sum of the exterior angles of any polygon is always 360 degrees. Each exterior angle is formed by extending one side of the polygon, and the sum of all these exterior angles will always be 360 degrees.
49.
The interior sum of a quadrilateral is ____.
Correct Answer
D. 360
Explanation
The interior sum of a quadrilateral is 360 because a quadrilateral has four angles, and the sum of the interior angles of any polygon is given by the formula (n-2) * 180, where n is the number of sides. In this case, (4-2) * 180 = 360.
50.
Find the measurement of the unknown interior angle.
Hint: Use the interior sum of a pentagon: 180 x (number of sides - 2).* SHOW YOUR WORK *
Correct Answer
A. 95
Explanation
The correct answer is 95. To find the measurement of the unknown interior angle, we can use the formula for the interior sum of a polygon, which states that the sum of all interior angles of a polygon is equal to 180 multiplied by the number of sides minus 2. Since a pentagon has 5 sides, we can substitute this value into the formula: 180 x (5 - 2) = 180 x 3 = 540. Since all the known interior angles of the pentagon add up to 540 degrees, we can find the measurement of the unknown angle by subtracting the sum of the known angles from 540. In this case, the sum of the known angles is 445 degrees (100 + 75 + 135 + 80), so the unknown angle is 540 - 445 = 95 degrees.