NAME DATE PERIOD Lesson 1 Homework Practice - …serray.weebly.com/uploads/4/2/9/3/42933991/chapter_5_packet_8th...NAME _____ DATE _____ PERIOD _____ ... Lesson 3 Homework Practice
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Course 3 • Chapter 5 Triangles and the Pythagorean Theorem 73
NAME _____________________________________________ DATE __________________ PERIOD _________
For Exercises 1–6, use the figure at the right. In the figure, line m is parallel to line n.
List all pairs of each type of angle.
1. vertical
2. complementary
3. supplementary
4. corresponding
5. alternate interior
6. alternate exterior
Use the figure at the right for Exercises 7–10.
7. Find the measure of ∠2. Explain your reasoning.
8. Find the measure of ∠3. Explain your reasoning.
9. Find the measure of ∠4. Explain your reasoning.
10. Find the measure of ∠6. Explain your reasoning.
11. ALGEBRA Angles A and B are corresponding angles formed by two parallel lines cut by a transversal. If m∠A = 4x and m∠B = 3x + 7, find the value of x. Explain.
12. ALGEBRA Angles G and H are supplementary and congruent. If ∠G and ∠H are alternate interior angles, what is the measure of each angle?
NAME _____________________________________________ DATE ____________________________ PERIOD ____________
Course 3 • Chapter 5 Triangles and the Pythagorean Theorem 75
Lesson 2 Homework Practice
Geometric Proof
Complete a paragraph proof.
1. Given: Two intersecting lines with m∠1 = 6x + 45 and
m∠3 = 9x + 15
Prove: x = 10
2. Given: Lines a and b are perpendicular.
Prove: ∠3 and ∠4 are complementary.
3. Given: ∠1 and ∠2 are a linear pair; m∠1 = 120°
Prove: ∠2 is acute.
NAME _____________________________________________ DATE ____________________________ PERIOD ____________
Course 3 • Chapter 5 Triangles and the Pythagorean Theorem 77
Lesson 3 Homework Practice
Angles of Triangles Find the value of x in each triangle.
1. 2. 3.
4. 5. 6.
Find the missing measure in each triangle with the given angle measures.
7. 45°, 35°, x° 8. 100°, x°, 40° 9. x°, 90°, 16°
10. Find the third angle of a right triangle if one of the angles measures 24°, 11. What is the third angle of a right triangle if one of the angles measures 51°? 12. ALGEBRA Find m∠A in ABC if m∠B = 38° and m∠C = 38°, 13. ALGEBRA In XYZ, m∠Z = 113° and m∠X = 28°, What is m∠Y?
Classify the marked triangle in each object by its angles and by its sides.
14. 15. 16.
ALGEBRA Find the value of x in each triangle.
17. 18. 19.
Course 3 • Chapter 5 Triangles and the Pythagorean Theorem 79
NAME _____________________________________________ DATE __________________ PERIOD _________
Find the sum of the interior angle measures of each polygon.
1. pentagon 2. decagon 3. 16-gon
4. 18-gon 5. 30-gon 6. 34-gon
Find the measure of one interior angle in each regular polygon. Round to the nearest tenth if necessary.
7. pentagon 8. octagon 9. 24-gon
ALGEBRA For Exercises 10 and 11, determine the angle measures in each polygon.
10. 5x°
x° 5x°
x° 11.
135°
x°
135°
x°
x°
12. FLOORING A floor is tiled with a pattern consisting of regular octagons and squares as shown. Find the measure of each angle at the circled vertex. Then find the sum of the angles.
13. ART Rachaunn is laying out a pattern for a stained glass window. So far he has placed the 13 regular polygons shown. Find the measure of each angle at the circled vertex. Then find the sum of the angles.
14. REASONING Vanessa’s mother made a quilt using a pattern of repeating regular hexagons as shown. Will Vanessa be able to make a similar quilt with a pattern of repeating regular pentagons? Explain your reasoning.