Lesson Warm Up 76 1. translation 2. translation 5 left
Lesson
76
Warm Up 76 1. translation 2. translation 5 left and 3 up 3. A Lesson Practice 76 a. Yes, it has five lines of symmetry. b. 5; 72° c. Yes; the triangle would have a line of symmetry on the x-axis. d. A 50-sided polygon would have 50 lines of symmetry.
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 76–1
Saxon Geometry
Lesson Practice 76
5.
Triangle
3
Quadrilateral
4
Pentagon
5
Hexagon
6
Heptagon
7
Octagon
8
Nonagon
9
Decagon
10
3. J(-2, 3); K(-2, 5); L(-4, 4)
D x
-8
2. Rotational symmetry in regular polygons resembles lines of symmetry: the order is equal to the number of sides in the polygon. Regular Polygon
y
4
1 or 0.1 1. approximately _ 10
Order of Rotational Symmetry
8
76
-4
O
4
8
-4 -8
6. QS = 11.3 ft 7. The longer diagonal. 8. If LM = LN, then m∠N = m∠M by the Isosceles Triangle Theorem. That expression contradicts the given information, so LM ≠ LN. 9. There is no rotational symmetry in this symbol because when you rotate it 180°, the blue and white sides have switched. 10. 4 feet per second 11. 100 cm2
4. B 12. area of one triangle = 1 _ as; area of six triangles 2 1 =6 _ as = 3as 2
(
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 76–2
)
Saxon Geometry
Lesson 13. Angle-Angle Similarity Postulate
25. Sample: Since tangent sin is equal to _ cos , and cos 90° is 0, the denominator of tangent is 0 at 90°. Another degree measure for which the tangent is undefined is 270°.
14. yes, x = 0 15. x = 26; y = 16 16. A 17. Equation of C is (x - 1)2 + (y - 1)2 = 25; (6 - 1)2 + (1 - 1)2 = 2 2 5 + 0 = 25; (4 -1)2+ 2 2 (5 - 1) 2 = 3 + 4 = 25
26. y = 3.2 27. 0.24 km 28. (-2, -2)
18. z = 2 19. 1505 cm
2
20. 522 meters 21. no; yes, 90°, order 4; no 22. E = (3, 0)
29. No; Magnitude is an absolute value, so it is impossible for magnitude to have an opposite value. y M(1, 11)
30. 10 8
23. GE = 16, GF = 15, m∠DFG = 65°, and m∠GDE = 130°
R(4, 11) W(4, 8)
K(1, 8)
y=x+2
W´(6, 6) R´(9, 6)
6 4
K´(6, 3)
2
M´(9, 3) x
24. B
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
76
O
LSN 76–3
2
4
6
8
Saxon Geometry
76
Warm Up 76 1. translation 2. translation 5 left and 3 up 3. A Lesson Practice 76 a. Yes, it has five lines of symmetry. b. 5; 72° c. Yes; the triangle would have a line of symmetry on the x-axis. d. A 50-sided polygon would have 50 lines of symmetry.
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 76–1
Saxon Geometry
Lesson Practice 76
5.
Triangle
3
Quadrilateral
4
Pentagon
5
Hexagon
6
Heptagon
7
Octagon
8
Nonagon
9
Decagon
10
3. J(-2, 3); K(-2, 5); L(-4, 4)
D x
-8
2. Rotational symmetry in regular polygons resembles lines of symmetry: the order is equal to the number of sides in the polygon. Regular Polygon
y
4
1 or 0.1 1. approximately _ 10
Order of Rotational Symmetry
8
76
-4
O
4
8
-4 -8
6. QS = 11.3 ft 7. The longer diagonal. 8. If LM = LN, then m∠N = m∠M by the Isosceles Triangle Theorem. That expression contradicts the given information, so LM ≠ LN. 9. There is no rotational symmetry in this symbol because when you rotate it 180°, the blue and white sides have switched. 10. 4 feet per second 11. 100 cm2
4. B 12. area of one triangle = 1 _ as; area of six triangles 2 1 =6 _ as = 3as 2
(
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
LSN 76–2
)
Saxon Geometry
Lesson 13. Angle-Angle Similarity Postulate
25. Sample: Since tangent sin is equal to _ cos , and cos 90° is 0, the denominator of tangent is 0 at 90°. Another degree measure for which the tangent is undefined is 270°.
14. yes, x = 0 15. x = 26; y = 16 16. A 17. Equation of C is (x - 1)2 + (y - 1)2 = 25; (6 - 1)2 + (1 - 1)2 = 2 2 5 + 0 = 25; (4 -1)2+ 2 2 (5 - 1) 2 = 3 + 4 = 25
26. y = 3.2 27. 0.24 km 28. (-2, -2)
18. z = 2 19. 1505 cm
2
20. 522 meters 21. no; yes, 90°, order 4; no 22. E = (3, 0)
29. No; Magnitude is an absolute value, so it is impossible for magnitude to have an opposite value. y M(1, 11)
30. 10 8
23. GE = 16, GF = 15, m∠DFG = 65°, and m∠GDE = 130°
R(4, 11) W(4, 8)
K(1, 8)
y=x+2
W´(6, 6) R´(9, 6)
6 4
K´(6, 3)
2
M´(9, 3) x
24. B
© 2009 Saxon®, an imprint of HMH Supplemental Publishers Inc. All rights reserved.
76
O
LSN 76–3
2
4
6
8
Saxon Geometry
