000200010271713722_CH06_L01.qxp Name 2/5/13 6:31 PM Page 2 Class Date Reteaching 6-1 Angle Measures Acute angles have a measurement of less than 90. In the diagram below, &1 and &2 are acute angles. Obtuse angles have a measurement of more than 90. In the diagram, &5 is an obtuse angle. Vertical angles are formed across from each other where two lines intersect. They always have equal measurements. In the diagram, &1 and &4 are vertical angles. They both measure 50. 3 2 50 1 4 5 All rights reserved. When the sum of two angles is 90, the angles are complementary. In the diagram, &1 and &2 are complementary angles. To find the measurement of a complementary angle, subtract from 90. 90 - m&1 = m&2 90 - 50 = m&2 40 = m&2 m&2 = 40 When the sum of two angles is 180, the angles are supplementary. In the diagram, &4 and &5 are supplementary angles. To find the measurement of a supplementary angle, subtract from 180. 180 - 50 = m&5 130 = m&5 m&5 = 130 Use the diagram to find the measurement of each angle. Then classify each angle as obtuse, right, or acute. 146 A 1. &A 2. &B B C D 40 3. &C 4. &D 5. Angles 1 and 2 are supplementary. If angle 1 measures (2x 2)°, and angle 2 measures (x 5)°, what is the measure of each angle? Course 2 Lesson 6-1 Reteaching © Pearson Education, Inc., publishing as Pearson Prentice Hall. 180 - m&4 = m&5 2/5/13 5:10 PM Page 2 Name Class Date Reteaching 6-2 Area of a Parallelogram You can use the area of a rectangle to find the area of a parallelogram. 1 2 3 4 cm Draw a perpendicular segment from one vertex to the opposite side to form a triangle. 8 cm Move the triangle to the right side of the parallelogram to form a rectangle. 4 cm Find the area of the rectangle. A = length width = base height = bh 8 cm A = bh A=8?4 A = 32 cm2 The parallelogram has the same base, height, and area as the rectangle. All rights reserved. 000200010271713722_CH06_L02.qxd Find the area of each figure. 1. 2. 6 cm 3. 5m 5 cm 8 ft 7m 4. 5. 4.3 in. 6. 0.7 ft 3.6 in. 2.1 in. 0.9 ft 7.2 in. Find the area of a parallelogram with base length b and height h. 7. b 7 in., h 4 in. Course 2 Lesson 6-2 8. b 9 m, h 1.5 m 9. b 1.25 cm, h 2 cm Reteaching © Pearson Education, Inc., publishing as Pearson Prentice Hall. 4 ft 000200010271713722_CH06_L03.qxd 2/6/13 11:15 AM Name Page 2 Class Date Reteaching 6-3 Area of a Triangle You can use the area of a parallelogram to find the area of a triangle. Two identical triangles, together as shown, form a parallelogram. Each triangle has half the area of the parallelogram. 4 cm Area of parallelogram: A bh Area of triangle: A 1 2 bh 1 2 7 cm ? 7 ? 4 14 cm2 This triangle has an area of 14 cm2. 1. 2. 3.2 ft 10 cm 6 cm All rights reserved. Find the area of each triangle. 3. 3.2 m 3.2 ft 5m 4. 7.8 cm Solve. 5. Ryan took measurements of his new kite and made the drawing shown on the right. in. 6 . 7 4.1 in. What is the area of Ryan’s kite? in. 12.4 17.4 in. 10.3 in. Course 2 Lesson 6-3 Reteaching © Pearson Education, Inc., publishing as Pearson Prentice Hall. 9 cm 000200010271713722_CH06_L04.qxd 3/20/13 9:09 PM Page 2 Name Class Date Reteaching 6-4 Areas of Other Figures Trapezoid Irregular Figures Two identical trapezoids, together as shown, form a parallelogram. The trapezoid has half the area of the parallelogram. Not all geometric figures are shapes with which you are familiar. Some of them, however, can be 7 ft divided into familiar shapes. Find the area of the figure. 6 ft 10 ft Use the area formulas to find the areas of the triangle and the rectangle. 5 12 (2)(4) A 5 12 h(b1 1 b2) Area of trapezoid: 5 12bh 5 12 (8) 5 12 (4)(10 1 8) 4 ft 2 ft 7 ft 5 4 ft2 ⫽ 2(18) ⫽ 36 in.2 All rights reserved. Area of a triangle Area of parallelogram: A 5 (b1 1 b2)h 9 ft Area of a rectangle ⫽ bh ⫽ (7)(10) ⫽ 70 ft2 10 ft Total area ⫽ area of triangle ⫹ area of rectangle ⫽ 4 ⫹ 70 ⫽ 74 The total area is 74 ft2. Based on appearance, find the area of each figure. 1. 2. 48 ft 22 ft 4 ft 7 ft 3. 3 12 in. 9 12 in. 20 ft 6 ft 4. 5. 7m 6. 26 km 4m 17 km 11 m Course 2 Lesson 6-4 36 yd 37 yd 11 km 46 km 13 m 20 yd 80 yd Reteaching © Pearson Education, Inc., publishing as Pearson Prentice Hall. Find the total area by adding the area of each figure. 000200010271713722_CH06_L05.qxd 2/5/13 5:09 PM Page 2 Name Class Reteaching 6-5 Date Circumference and Area of a Circle The circumference of a circle is the distance around it. To find the circumference of a circle with radius r and diameter d, use either the formula C = 2pr or C = pd. Use 3.14 for p. d ⫽ 8 cm C ⫽ pd ≈ 3.14 ? 8 ⫽ 25.12 cm 6 ft To the nearest centimeter, the circumference is 25 cm. To the nearest foot, the circumference is 38 ft. All rights reserved. 8 cm r ⫽ 6 ft C ⫽ 2pr ≈ 2 ? 3.14 ? 6 ⫽ 37.68 ft To find the area of a circle, use A ⫽ pr2. The diameter of the circle is 8 cm, so the radius is 4 cm. 8 cm A = pr2 ≈ 3.14 ? 4 ? 4 ⫽ 50.24 cm2 To the nearest square centimeter, the area is 50 cm2. 2. 3. in . 1. © Pearson Education, Inc., publishing as Pearson Prentice Hall. Find the circumference and area of each circle. Round your answer to the nearest whole unit. 4. 10 2 7 cm 5. m 6. 2 cm 8y d 3 ft Course 2 Lesson 6-5 Reteaching

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