Geometry Tutor Worksheet 4 Intersecting Lines
Geometry Tutor Worksheet 4 Intersecting Lines
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Geometry Tutor - Worksheet 4 – Intersecting Lines
1. What is the measure of the angle that is formed when two perpendicular lines intersect?
2. What is the difference between a postulate and a theorem?
3. True or False. The definition of parallel lines is two lines that never intersect.
4. When two parallel lines are cut by a transversal, alternate interior angles are ______.
5. When two parallel lines are cut by a transversal, same side interior angles are ______.
6. When two parallel lines are cut by a transversal, alternate exterior angles are ______.
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7. Suppose two parallel lines are cut by a transversal. One of the angles formed has a measure of 74°. What is the measure of another angle formed that has a different measure?
8. In the figure below, name the pairs of corresponding angles.
9. In the figure below, name the pairs of alternate interior angles.
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10. In the figure below, name the pairs of alternate exterior angles.
11. In the figure below, name the pairs of same side interior angles.
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12. Solve for 𝑥 using the line and angle relationships in this figure.
13. Solve for 𝑥 using the line and angle relationships in this figure.
14. What is the value of 𝑥?
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15. What is the value of 𝑥?
16. What is the value of 𝑤?
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17. Solve for 𝑥 using the line and angle relationships in this figure.
18. What is the value of 𝑧?
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19. Solve for 𝑥 using the line and angle relationships in this figure.
20. Solve for 𝑥 using the line and angle relationships in this figure.
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21. Solve for 𝑥 using the line and angle relationships in this figure.
22. Solve for 𝑥 using the line and angle relationships in this figure.
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23. Solve for 𝑥 using the line and angle relationships in this figure.
24. Solve for 𝑥 using the line and angle relationships in this figure.
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Answers - Geometry Tutor - Worksheet 4 – Intersecting Lines 1. What is the measure of the angle that is formed when two perpendicular lines intersect? Perpendicular lines intersect at right angles. Thus, their intersection forms angles that have a measure of 90°. Answer: 90°
2. What is the difference between a postulate and a theorem? Answer: A postulate is a statement of fact that is accepted as true. A theorem is a statement that is accepted as true after it is proven.
3. True or False. The definition of parallel lines is two lines that never intersect. Two lines are parallel if they are on the same plane and never intersection. Two lines that are not on the same plane are called “skew” lines. Answer: False
4. When two parallel lines are cut by a transversal, alternate interior angles are ______. Answer: congruent
5. When two parallel lines are cut by a transversal, same side interior angles are ______. Answer: supplementary
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6. When two parallel lines are cut by a transversal, alternate exterior angles are ______. Answer: congruent
7. Suppose two parallel lines are cut by a transversal. One of the angles formed has a measure of 74°. What is the measure of another angle formed that has a different measure? When two parallel lines are cut by a transversal, the angles formed are either congruent or supplementary. Thus, if one angle has a measure of 74°, then all of the other angles have measures of either 74° or 106°. Answer: 106°
8. In the figure below, name the pairs of corresponding angles.
Answer: ∠1 and ∠5, ∠3 and ∠7, ∠2 and ∠6, ∠4 and ∠8
9. In the figure below, name the pairs of alternate interior angles.
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Answer: ∠4 and ∠5, ∠3 and ∠6
10. In the figure below, name the pairs of alternate exterior angles.
Answer: ∠1 and ∠8, ∠2 and ∠7
11. In the figure below, name the pairs of same side interior angles.
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Answer: ∠4 and ∠6, ∠3 and ∠5
12. Solve for 𝑥 using the line and angle relationships in this figure.
The angles involved are same side exterior angles, so they are supplementary, but in this case also congruent. This gives the equation 21𝑥 + 6 = 90. Solving for 𝑥; 21𝑥 = 84, 𝑥 = 4. Answer: 4
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13. Solve for 𝑥 using the line and angle relationships in this figure.
The angles involved are same alternate exterior angles, so they are congruent. This gives the equation 8𝑥 − 4 = 60. Solving for 𝑥; 8𝑥 = 64, 𝑥 = 8. Answer: 8
14. What is the value of 𝑥?
The angles involved are alternate interior angles, so they are congruent. Thus, 𝑥 = 84°. Answer: 84°
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15. What is the value of 𝑥?
The angles involved are alternate exterior angles, so they are congruent. Thus, 𝑥 = 110°. Answer: 110°
16. What is the value of 𝑤?
The angles involved are corresponding angles, so they are congruent. Thus, 𝑤 = 53°. Answer: 53°
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17. Solve for 𝑥 using the line and angle relationships in this figure.
The angles involved are corresponding angles, so they are congruent. This gives the equation 21𝑥 + 5 = 23𝑥 − 5. Solving for 𝑥; 2𝑥 = 10, 𝑥 = 5. Answer: 5
18. What is the value of 𝑧?
The angles involved are alternate interior angles, so they are congruent. Thus, 𝑧 = 100°. Answer: 100°
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19. Solve for 𝑥 using the line and angle relationships in this figure.
The angles involved are alternate interior angles, so they are congruent. This gives the equation 𝑥 + 139 = 132. Solving for 𝑥; 𝑥 = −7. Answer: −7
20. Solve for 𝑥 using the line and angle relationships in this figure.
The angles involved are same side interior angles, so they are supplementary. This gives the equation 20𝑥 + 5 + 24𝑥 − 1 = 180. Solving for 𝑥; 44𝑥 + 4 = 180, 44𝑥 = 176, 𝑥 = 4. Answer: 4
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21. Solve for 𝑥 using the line and angle relationships in this figure.
The angles involved are corresponding angles, so they are congruent. This gives the equation 5𝑥 + 10 = 6𝑥. Solving for 𝑥; 𝑥 = 10. Answer: 10
22. Solve for 𝑥 using the line and angle relationships in this figure.
The angles involved are same side interior angles, so they are supplementary. This gives the equation 𝑥 + 96 + 𝑥 + 96 = 180. Solving for 𝑥; 2𝑥 + 192 = 180, 2𝑥 = −12, 𝑥 = −6. Answer: −6
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23. Solve for 𝑥 using the line and angle relationships in this figure.
The angles involved are corresponding angles, so they are congruent. This gives the equation 75 = 11𝑥 − 2. Solving for 𝑥; 11𝑥 = 77, 𝑥 = 7. Answer: 7
24. Solve for 𝑥 using the line and angle relationships in this figure.
The angles involved are alternate exterior angles, so they are congruent. This gives the equation 12𝑥 + 17 = 14𝑥 − 1. Solving for 𝑥; 2𝑥 = 18, 𝑥 = 9. Answer: 9
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Geometry Tutor - Worksheet 4 – Intersecting Lines
1. What is the measure of the angle that is formed when two perpendicular lines intersect?
2. What is the difference between a postulate and a theorem?
3. True or False. The definition of parallel lines is two lines that never intersect.
4. When two parallel lines are cut by a transversal, alternate interior angles are ______.
5. When two parallel lines are cut by a transversal, same side interior angles are ______.
6. When two parallel lines are cut by a transversal, alternate exterior angles are ______.
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7. Suppose two parallel lines are cut by a transversal. One of the angles formed has a measure of 74°. What is the measure of another angle formed that has a different measure?
8. In the figure below, name the pairs of corresponding angles.
9. In the figure below, name the pairs of alternate interior angles.
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10. In the figure below, name the pairs of alternate exterior angles.
11. In the figure below, name the pairs of same side interior angles.
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12. Solve for 𝑥 using the line and angle relationships in this figure.
13. Solve for 𝑥 using the line and angle relationships in this figure.
14. What is the value of 𝑥?
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15. What is the value of 𝑥?
16. What is the value of 𝑤?
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17. Solve for 𝑥 using the line and angle relationships in this figure.
18. What is the value of 𝑧?
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19. Solve for 𝑥 using the line and angle relationships in this figure.
20. Solve for 𝑥 using the line and angle relationships in this figure.
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21. Solve for 𝑥 using the line and angle relationships in this figure.
22. Solve for 𝑥 using the line and angle relationships in this figure.
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23. Solve for 𝑥 using the line and angle relationships in this figure.
24. Solve for 𝑥 using the line and angle relationships in this figure.
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Answers - Geometry Tutor - Worksheet 4 – Intersecting Lines 1. What is the measure of the angle that is formed when two perpendicular lines intersect? Perpendicular lines intersect at right angles. Thus, their intersection forms angles that have a measure of 90°. Answer: 90°
2. What is the difference between a postulate and a theorem? Answer: A postulate is a statement of fact that is accepted as true. A theorem is a statement that is accepted as true after it is proven.
3. True or False. The definition of parallel lines is two lines that never intersect. Two lines are parallel if they are on the same plane and never intersection. Two lines that are not on the same plane are called “skew” lines. Answer: False
4. When two parallel lines are cut by a transversal, alternate interior angles are ______. Answer: congruent
5. When two parallel lines are cut by a transversal, same side interior angles are ______. Answer: supplementary
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6. When two parallel lines are cut by a transversal, alternate exterior angles are ______. Answer: congruent
7. Suppose two parallel lines are cut by a transversal. One of the angles formed has a measure of 74°. What is the measure of another angle formed that has a different measure? When two parallel lines are cut by a transversal, the angles formed are either congruent or supplementary. Thus, if one angle has a measure of 74°, then all of the other angles have measures of either 74° or 106°. Answer: 106°
8. In the figure below, name the pairs of corresponding angles.
Answer: ∠1 and ∠5, ∠3 and ∠7, ∠2 and ∠6, ∠4 and ∠8
9. In the figure below, name the pairs of alternate interior angles.
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Answer: ∠4 and ∠5, ∠3 and ∠6
10. In the figure below, name the pairs of alternate exterior angles.
Answer: ∠1 and ∠8, ∠2 and ∠7
11. In the figure below, name the pairs of same side interior angles.
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Answer: ∠4 and ∠6, ∠3 and ∠5
12. Solve for 𝑥 using the line and angle relationships in this figure.
The angles involved are same side exterior angles, so they are supplementary, but in this case also congruent. This gives the equation 21𝑥 + 6 = 90. Solving for 𝑥; 21𝑥 = 84, 𝑥 = 4. Answer: 4
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13. Solve for 𝑥 using the line and angle relationships in this figure.
The angles involved are same alternate exterior angles, so they are congruent. This gives the equation 8𝑥 − 4 = 60. Solving for 𝑥; 8𝑥 = 64, 𝑥 = 8. Answer: 8
14. What is the value of 𝑥?
The angles involved are alternate interior angles, so they are congruent. Thus, 𝑥 = 84°. Answer: 84°
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15. What is the value of 𝑥?
The angles involved are alternate exterior angles, so they are congruent. Thus, 𝑥 = 110°. Answer: 110°
16. What is the value of 𝑤?
The angles involved are corresponding angles, so they are congruent. Thus, 𝑤 = 53°. Answer: 53°
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17. Solve for 𝑥 using the line and angle relationships in this figure.
The angles involved are corresponding angles, so they are congruent. This gives the equation 21𝑥 + 5 = 23𝑥 − 5. Solving for 𝑥; 2𝑥 = 10, 𝑥 = 5. Answer: 5
18. What is the value of 𝑧?
The angles involved are alternate interior angles, so they are congruent. Thus, 𝑧 = 100°. Answer: 100°
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19. Solve for 𝑥 using the line and angle relationships in this figure.
The angles involved are alternate interior angles, so they are congruent. This gives the equation 𝑥 + 139 = 132. Solving for 𝑥; 𝑥 = −7. Answer: −7
20. Solve for 𝑥 using the line and angle relationships in this figure.
The angles involved are same side interior angles, so they are supplementary. This gives the equation 20𝑥 + 5 + 24𝑥 − 1 = 180. Solving for 𝑥; 44𝑥 + 4 = 180, 44𝑥 = 176, 𝑥 = 4. Answer: 4
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21. Solve for 𝑥 using the line and angle relationships in this figure.
The angles involved are corresponding angles, so they are congruent. This gives the equation 5𝑥 + 10 = 6𝑥. Solving for 𝑥; 𝑥 = 10. Answer: 10
22. Solve for 𝑥 using the line and angle relationships in this figure.
The angles involved are same side interior angles, so they are supplementary. This gives the equation 𝑥 + 96 + 𝑥 + 96 = 180. Solving for 𝑥; 2𝑥 + 192 = 180, 2𝑥 = −12, 𝑥 = −6. Answer: −6
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23. Solve for 𝑥 using the line and angle relationships in this figure.
The angles involved are corresponding angles, so they are congruent. This gives the equation 75 = 11𝑥 − 2. Solving for 𝑥; 11𝑥 = 77, 𝑥 = 7. Answer: 7
24. Solve for 𝑥 using the line and angle relationships in this figure.
The angles involved are alternate exterior angles, so they are congruent. This gives the equation 12𝑥 + 17 = 14𝑥 − 1. Solving for 𝑥; 2𝑥 = 18, 𝑥 = 9. Answer: 9
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