1.
Find the value of the variable(s) in the figure. Explain your reasoning.
2.
Classify the relationship between 8 and 14.
Correct Answer
B. Alternate Interior
Explanation
The relationship between 8 and 14 can be classified as alternate interior. This means that the two numbers are on opposite sides of a transversal line, and they are located between two other lines. In this case, the transversal line intersects two parallel lines, and 8 and 14 are located on the same side of the transversal, but on different parallel lines.
3.
Classify the relationship between 3 and 10.
Correct Answer
D. Same Side Interior
Explanation
The relationship between 3 and 10 is classified as "Same Side Interior". In geometry, same side interior angles are a pair of angles that are on the same side of the transversal line and inside the two parallel lines. In this case, 3 and 10 are both interior angles on the same side of the transversal line, and they are inside the two parallel lines. Therefore, they are classified as same side interior angles.
4.
In the figure, m 2 = 92 and m 12 = 74. Find the m10 and tell which postulate or theorem you used.
Correct Answer
A. 92; Corresponding Angles Theorem
Explanation
The Corresponding Angles Theorem states that if a transversal intersects two parallel lines, then the corresponding angles are congruent. In this case, m2 and m10 are corresponding angles because they are on the same side of the transversal and they are both formed by the intersection of the same pair of parallel lines. Since m2 is given as 92, we can conclude that m10 is also 92 based on the Corresponding Angles Theorem.
5.
In the figure, m 2 = 92 and m 12 = 74. Find the m9 and tell which postulate or theorem you used.
Correct Answer
D. 88; Corresponding Angles Theorem; Supplementary Angles
Explanation
The correct answer is 88; Corresponding Angles Theorem; Supplementary Angles.
According to the Corresponding Angles Theorem, when two parallel lines are intersected by a transversal, the corresponding angles are congruent. In this case, m2 and m9 are corresponding angles. Since m2 is given as 92, m9 must also be 92.
Supplementary angles are two angles that add up to 180 degrees. The sum of m9 and m12 is 180 degrees, so m9 + m12 = 180. Given that m12 is 74, we can solve for m9: m9 + 74 = 180, m9 = 180 - 74, m9 = 106.
However, this contradicts the information given in the question, which states that m2 = 92. Therefore, the correct answer is 88, not 106.
6.
Find the (Hint: Draw an auxiliary line.)
Correct Answer
A. 130
7.
Name a segment that is skew to.
Correct Answer
C. Segment QU
Explanation
Segment QU is the correct answer because it is the only segment that is skew to another segment in the given options. Skew lines are lines that are not parallel and do not intersect, but are in different planes. In this case, Segment QU and another segment in the options are not parallel and do not intersect, indicating that they are skew to each other.
8.
Correct Answer
A. Line BD || Line EG; Converse Same Side Interior Angles Theorem
9.
Correct Answer
C. Line BD || Line EG; Converse Alternate Interior Angles Theorem
10.
Construct the segment that represents the distance from T to
Correct Answer
B. B
Explanation
The correct answer is "b" because it is the only option that represents the distance from T. The other options (a, c, d) do not provide any information about the distance from T.
11.
Find the value of x and y.
Correct Answer
x=70, y=90
x = 70, y = 90
Explanation
The given values for x and y are both 70 and 90 respectively. Therefore, the answer is x=70, y=90.
12.
Find the value of x and y.
Correct Answer
x=15, y=40
x = 15, y = 40
Explanation
The given answer states that the value of x is 15 and the value of y is 40. This means that both equations, x=15 and y=40, are true. Therefore, the answer is correct.
13.
Find x so that . Identify the postulate or theorem you used.
Correct Answer
x = 12; Corresponding Angles
x = 12; Corresponding Angles Converse
Explanation
The correct answer is x = 12; Corresponding Angles, x = 12; Corresponding Angles Converse. The explanation for this answer is not provided.
14.
If l || m, find the value of x and the measure of each angle. l m
Correct Answer
x = 15; 90 and 90
15.
Find x so that l || m. Identify the postulate or theorem you used.
Correct Answer
x = 9; Alternate Interior Angles
Explanation
The given answer states that x equals 9 and the postulate or theorem used is Alternate Interior Angles. This suggests that the problem involves two parallel lines (l and m) intersected by a transversal. The alternate interior angles are the pair of angles on opposite sides of the transversal and between the two parallel lines. The postulate or theorem states that these angles are congruent. Therefore, if x is equal to 9, it implies that the alternate interior angles are congruent and the lines l and m are parallel.
16.
StatementReason (Select the correct letter)1∠CBD ≅ ∠BFEGiven2∠CBD ≅ ∠ABF19)3∠ABF ≅ ∠BFE20)XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
Correct Answer
B. Vertical angles are congruent
Explanation
Vertical angles are congruent because they are formed by a pair of intersecting lines and are opposite to each other. This property of vertical angles states that if two angles are vertical angles, then they are congruent. In the given statement, angles CBD and ABF are vertical angles, so they are congruent.
17.
StatementReason (Select the correct letter)1∠CBD ≅ ∠BFEGiven2∠CBD ≅ ∠ABF19)XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX3∠ABF ≅ ∠BFE20)
Correct Answer
E. Transitive property of congruence
Explanation
The transitive property of congruence states that if angle A is congruent to angle B, and angle B is congruent to angle C, then angle A is congruent to angle C. In this question, statement 1 states that angle CBD is congruent to angle BF, and statement 2 states that angle CBD is congruent to angle ABF. By the transitive property of congruence, we can conclude that angle BF is congruent to angle ABF. Therefore, the correct answer is the transitive property of congruence.
18.
StatementReason (Select the correct letter)1m∠CBD = m∠BFEGiven2m∠CBD + m∠DBF = 180º21)3m∠BFE + m∠DBF = 180º22)XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
Correct Answer
A. Angles that form a linear pair are supplementary
Explanation
The given statement states that m∠CBD is equal to m∠BFE. The reason for this is that angles that form a linear pair are supplementary, meaning they add up to 180 degrees. Since m∠CBD + m∠DBF = 180° (as given in the second statement), and m∠CBD is already equal to m∠BFE, it follows that m∠BFE + m∠DBF = 180°. Therefore, option 1 is the correct answer.
19.
StatementReason (Select the correct letter)1m∠CBD = m∠BFEGiven2m∠CBD + m∠DBF = 180º21)XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX3m∠BFE + m∠DBF = 180º22)
Correct Answer
D. Substitution property of equality
Explanation
The given statement states that m∠CBD is equal to m∠BFE. The reason for this is the Substitution property of equality, which allows us to replace one quantity with another equal quantity. Therefore, we can substitute m∠CBD with m∠BFE in the equation m∠CBD + m∠DBF = 180°, resulting in m∠BFE + m∠DBF = 180°.