Lesson Warm Up 33 1. converse 2. 5 3. If two angles are congruent ...
Lesson
33
Warm Up 33 1. converse 2. 5 3. If two angles are congruent, then they are vertical angles; no Lesson Practice 33 329 a. √ b. no c. obtuse d. right e. No. 62 + 7.52 < 102, so the triangle is obtuse.
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 33–1
Saxon Geometry
Lesson Practice 33
33
By substitution, m∠UVS - m∠UVT = m∠UTV. By the Transitive Property of Equality, m∠SVT = m∠UTV, and by the definition of congruent angles, ∠SVT ∠UTV.
1. ∠F ∠T, ∠G _ ∠U, _ ∠H _ ∠V, _ FG _ TU _, GH UV , HF VT 2. Yes. By the Triangle Angle Sum Theorem, m∠DEF = 52°, so the triangles are congruent by the ASA Theorem.
6. No, the included angle is different.
2 ; x > 2 √ 2 3. x = 2 √
7. 6xy
4. If a triangle is obtuse, then it is isosceles.
8. a. obtuse; 201.6 feet b. acute; 223.3 feet
5. Since ∠STU and ∠UVS are congruent, m∠STU = m∠UVS, by definition of congruent angles. ∠STV and ∠TVU must also have the same measure, for the same reason. By the Angle Addition Postulate, m∠STU = m∠STV + m∠UTV, and m∠UVS = m∠UVT + m∠SVT. By the Subtraction Property of Equality, m∠STU - m∠STV = m∠UTV, and m∠UVS m∠UVT = m∠SVT. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 33–2
9. If a triangle has an obtuse angle, then it is not acute; inverse; any right triangle is a counterexample for the statement, but a triangle cannot have an obtuse angle if it is acute.
Saxon Geometry
Lesson 10. H is the midpoint of GI Given
GH HI Definition of midpoint
EF HI Given
EF GH Transitive Property of Congruence
11. a. an infinite number
33
b. A volcano is active or it is not expected to erupt again; No, because a volcano might be dormant, and thus it is not active but is expected to erupt again.
b. They all have the same measure. 2 12. x < 6 √ 13. For each increase of 1 in x, y increases by m; use this fact to plot two or three points, starting at the y-intercept, (0, b). 14. a. A volcano is active and not expected to erupt again; No, because by definition, an active volcano is expected to erupt again.
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 33–3
Saxon Geometry
Lesson 15.
1 _ ((x + 1) + (x + 5))(x) = 40 2
1 _ (2x + 6)(x) = 40 2
33
Area of a trapezoid Simplify.
2 Distributive Property x + 3x = 40 2 x + 3x - 40 = 40 - 40 Subtraction Property of Equality 2 Simplify. x + 3x - 40 = 0 (x + 8)(x - 5) = 0 Factor. x-5=0 x>0 x-5+5=5 Addition Property of Equality x=5 Simplify. Base 1 = 5 + 1 = 6 ft Base 2 = 5 + 5 = 10 ft
16. A 17. interior: ∠EDC, ∠ABC, and ∠BAF; exterior: ∠CDJ and ∠LFE 18. x = 34 19. a 1 = 2'1''; a 2 = 4'2''; a 3 = 6'3''; a 4 = 8'5'' 20. The student used the Law of Syllogism when it did not apply; b is a true statement. 21. 30° 22. The other remote interior angle measures 136° - 56° = 80° (Exterior Angle Theorem); 3rd interior angle measures 180° - (56° + 80°) = 44° (Triangle Angle Sum Theorem) © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 33–4
Saxon Geometry
Lesson
33
23. x = 14 24. Substitute -1 for m, (4, 5) for (x 1, y 1), and (x, y) for (x 2, y 2) into the slope formula; cross-multiply to clear the denominator and simplify. 25. 41 26. 126 27. 3.5 yards 28. 56° 29. (2.5, 4) 30. 14πx
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 33–5
Saxon Geometry
33
Warm Up 33 1. converse 2. 5 3. If two angles are congruent, then they are vertical angles; no Lesson Practice 33 329 a. √ b. no c. obtuse d. right e. No. 62 + 7.52 < 102, so the triangle is obtuse.
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 33–1
Saxon Geometry
Lesson Practice 33
33
By substitution, m∠UVS - m∠UVT = m∠UTV. By the Transitive Property of Equality, m∠SVT = m∠UTV, and by the definition of congruent angles, ∠SVT ∠UTV.
1. ∠F ∠T, ∠G _ ∠U, _ ∠H _ ∠V, _ FG _ TU _, GH UV , HF VT 2. Yes. By the Triangle Angle Sum Theorem, m∠DEF = 52°, so the triangles are congruent by the ASA Theorem.
6. No, the included angle is different.
2 ; x > 2 √ 2 3. x = 2 √
7. 6xy
4. If a triangle is obtuse, then it is isosceles.
8. a. obtuse; 201.6 feet b. acute; 223.3 feet
5. Since ∠STU and ∠UVS are congruent, m∠STU = m∠UVS, by definition of congruent angles. ∠STV and ∠TVU must also have the same measure, for the same reason. By the Angle Addition Postulate, m∠STU = m∠STV + m∠UTV, and m∠UVS = m∠UVT + m∠SVT. By the Subtraction Property of Equality, m∠STU - m∠STV = m∠UTV, and m∠UVS m∠UVT = m∠SVT. © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 33–2
9. If a triangle has an obtuse angle, then it is not acute; inverse; any right triangle is a counterexample for the statement, but a triangle cannot have an obtuse angle if it is acute.
Saxon Geometry
Lesson 10. H is the midpoint of GI Given
GH HI Definition of midpoint
EF HI Given
EF GH Transitive Property of Congruence
11. a. an infinite number
33
b. A volcano is active or it is not expected to erupt again; No, because a volcano might be dormant, and thus it is not active but is expected to erupt again.
b. They all have the same measure. 2 12. x < 6 √ 13. For each increase of 1 in x, y increases by m; use this fact to plot two or three points, starting at the y-intercept, (0, b). 14. a. A volcano is active and not expected to erupt again; No, because by definition, an active volcano is expected to erupt again.
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 33–3
Saxon Geometry
Lesson 15.
1 _ ((x + 1) + (x + 5))(x) = 40 2
1 _ (2x + 6)(x) = 40 2
33
Area of a trapezoid Simplify.
2 Distributive Property x + 3x = 40 2 x + 3x - 40 = 40 - 40 Subtraction Property of Equality 2 Simplify. x + 3x - 40 = 0 (x + 8)(x - 5) = 0 Factor. x-5=0 x>0 x-5+5=5 Addition Property of Equality x=5 Simplify. Base 1 = 5 + 1 = 6 ft Base 2 = 5 + 5 = 10 ft
16. A 17. interior: ∠EDC, ∠ABC, and ∠BAF; exterior: ∠CDJ and ∠LFE 18. x = 34 19. a 1 = 2'1''; a 2 = 4'2''; a 3 = 6'3''; a 4 = 8'5'' 20. The student used the Law of Syllogism when it did not apply; b is a true statement. 21. 30° 22. The other remote interior angle measures 136° - 56° = 80° (Exterior Angle Theorem); 3rd interior angle measures 180° - (56° + 80°) = 44° (Triangle Angle Sum Theorem) © 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 33–4
Saxon Geometry
Lesson
33
23. x = 14 24. Substitute -1 for m, (4, 5) for (x 1, y 1), and (x, y) for (x 2, y 2) into the slope formula; cross-multiply to clear the denominator and simplify. 25. 41 26. 126 27. 3.5 yards 28. 56° 29. (2.5, 4) 30. 14πx
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 33–5
Saxon Geometry
