Awesome April Angles & Geometry Answer Keys

Transcription

1 Awesome April Angles & Geometry Answer Keys Lessons & Activities for middle school geometry 2013 Lindsay Perro Clipart by Scrappin Doodles

2 Week One - Angles Angles Notes Practice Worksheet Quiz

3 Name _Answer Key Date A F B E Parallel Lines Lines in a plane that never intersect. FB II EC Transversal A line that crosses two or more other lines. AD is a transversal. D Types of Angles Complementary Two angles that equal 90º. Supplementary Two angles that equal 180º. Interior Angles formed by a transversal and the lines it crosses, inside the parallel lines. Exterior Angles formed by a transversal and the lines it crosses, outside the parallel lines. Alternate Two angles formed by a transversal and the lines it crosses, on opposite sides of the transversal. Alternate angles have the same measurement. Corresponding Two angles on the same side of the transversal, on a different line. Corresponding angles have the same measurement. Vertical Two angles that share a vertex, but not a side. Vertical angles have the same measurement. C Lindsay Perro

4 Name Answer key Date A F B E 5 6 C 7 8 Use the diagram above to answer the following questions. Types of Angles: 1. Name one pair of corresponding angles. <1 &<5, <2 &<6, <3 &<7, <4 &<8 2. Name one pair of vertical angles. <1 &<4, <2 &<3, <6 &<7, <5 &<8 3. Name one pair of supplementary angles. <5 &<6, <5 &<7, <6 &<8, <7 &<8 4. List the two pairs of alternate interior angles. <3 &<6, <4 &<5 5. List all of the exterior angles. <1, <2, <7, <8 Angle Measurements: 1. If < 1 is 120º, what is the measure of <2? 2. If < 5 is 112º, what is the measure of <2? 112º 3. If < 7 is 60º, what is the measure of <2? 60º 4. If < 4 is 135º, what is the measure of <2? 45º 5. If < 6 is 53º, what is the measure of <2? 6. If < 1 is 104º, what is the measure of all of the other angles? < 1 = 104º < 2 = 76º < 3 = 76º < 4 = 104º < 5 = 104º < 6 = 76º 76º D <1 &<2, <1 &<3, <2 &<4, <2 &<3 104º < 7 = < 8 = 60º 127º Lindsay Perro

5 Name _ Answer key Date A F B 1. Using the diagram above, identify two pairs of each of the following types of angles: *Corresponding 1&5, 3&7, 2&6, 4&8 *Vertical 1&4, 2&3, 5&8, 7&6 *Alternate Interior 3 & 6, 4 & 5 *Alternate Exterior 1 & 8, 2 & 7 *Supplementary 1&3, 5&7, 7&8, 8&6, 4&2, 1&2 *Interior 3, 4, 5, 6 2. Using the diagram above, find the missing angle measurements: *If m<1 is 145, m<7 35 *If m<4 is 120, m<2 60 *If m<3 is 72, m<7 72 *If m<6 is 88, m< Complete each statement with the correct type of angle: Two angles that are joined at the vertex and have the same measurement are Vertical angles. Two angles whose sum equals 180 are called Supplementary angles. Angles that are inside the parallel lines along the transversal are Interior angles. Two angles that are on opposite sides of the transversal, inside the parallel lines are Alternate Interior angles. Angles that are on the same side of the transversal, on opposite parallel lines are called Corresponding angles. Two angles that are on opposite sides of the transversal, outside the parallel lines are Alternate Exterior angles. E D C Lindsay Perro

6 Week Two - Area Area Notes Area Practice Volume Notes Volume Practice

7 Let s Practice! Find the area of each given shape. Answer Key 1. Formula A = b h 2. Formula A = 6 m b₁ + b₂ 2 h 6 feet 9 m 10 m 10 feet Area 60 feet ² 12 m Area 81 m ² 3. Formula A = b h 4. Formula A = 1 2 b h 6 in 4 in 12 cm 8 in 7 cm Area 32 in² Area 41 cm² 5. Find the area of a square with a side length of 14 inches. A = 196 inches² 6. Find the area of a triangle with a base of 11 cm and a height of 6 cm. A = 33 cm² 7. Find the area of a parallelogram with a base of 22 m, a side length of 12 m and a height of 8 m. A = 176 m² 8. Find the area of a trapezoid with a height of 5 cm, a b₁ of 16cm, a b₂ of 4 cm and a side length of 10 cm. A = 50 cm² 9. Find the area of a rectangle with a base of 15 feet and a height of 20 feet. A = 300 feet² 2011 Lindsay Perro

8 Name Answer Key Date Find the area of each figure. Triangles: 1. b= 16 ft, h = 15 ft Area = 120 ft² 2. b = 12 cm, h = 9cm Area = 54 cm² 3. b = 3 in, h = 5 in Area = 7.5 in² 4. b = 4 m, h = 4 m Area = 8 m² 5. b = 7.9 cm, h = 8 cm Area = 31.6 cm² Parallelograms: The side (s) measurement is given as a distracter and not used to determine the area. 1. b = 12 cm, h = 3.2 cm, s = 4.2 cm Area = 38.4 cm² 2. b = 19.4 ft, h = 7.5 ft, s = 2.3 ft Area = ft² 3. b = 5 in, h = 10 in, s = 15 in Area = 50 in² 4. b = 15.9 yd, h = 24 yd, s = 20 yd Area = yd² 5. b = 12 m, h = 23 m, s = 25 m Area = 276 m² Lindsay Perro

9 Trapezoids: 1. b1 = 12 cm, h = 5 cm, b2 = 4.2 cm Area = 40.5 cm² 2. b1 = 15.4 ft, h = 7.5 ft, b2 = 12.6 ft Area = 105 ft² 3. b1 = 15 in, h = 10 in, b2 = 25 in Area = 200 in² 4. b1 = 11.2 yd, h = 42 yd, b2 = 10 yd Area = yd² 5. b1 = 15.5 m, h = 9 m, b2 = 10.5 m Area = 117 m² Lindsay Perro

10 Guided Practice: ANSWER KEY 1. Find the volume of the rectangular prism below. 5 cm Step 1: Find the area of the base. 8 cm 32 cm² 4 cm Step 2: Multiply the area of the base by the height. 160 cm³ Step 3: Be sure to include units and an exponents in your answer. Volume is always written in cubic units because it is the product of three measurements. 2. Find the volume of a rectangular prism given the following measurements: Length = 3 inches Width = 7 inches Height = 12 inches Step 1: Find the area of the base. 21 in² Step 2: Multiply the area of the base by the height. 252 in³ Step 3: Be sure to include units and an exponents in your answer. Volume is always written in cubic units because it is the product of three measurements Lindsay Perro

11 Independent Practice. Show your work! Answer Key 1. Find the volume of the given rectangular prism. 30 cm 5,400 cm³ 15 cm 2. Find the volume of a rectangular prism with the given measurements: Length = 2 in, Width = 3 in, Height = 4 in 24 in³ 12 cm 3. Find the volume of a rectangular box with the given measurements: Length = 4 ft Width = 3 ft, Height = 3 ft 36 ft³ 4. The dimensions of a rectangular prism are 24 ft x 20 ft x 15 ft. Find the volume. 7,200 ft³ 5. Find the volume of a rectangular box with a length of 4.5 feet, width of 5 feet and a height of 5.5 feet ft³ 6. The dimensions of a rectangular box are 4.4 inches, 5.6 inches, and 8.2 inches. Find the volume in³ 2011 Lindsay Perro

12 Name _Answer Key Date Flip For Volume! Determine the volume of each cube and rectangular prism. Find your answer in one of the three answer boxes # Answer 1 Answer 2 Answer 3 5 ft 1 15 ft³ 125 ft³ 25 ft³ 2 1,080 in³ 34 in³ 186 in³ 10 in 18 in 6 in 20 cm 3 1,920 cm³ 906 cm³ 40 cm³ 12 cm 8 cm 4 9 m³ 6 m³ 27 m³ 3 m 10 in in³ 1,000 in³ 100 in³ Lindsay Perro

13 # Answer 1 Answer 2 Answer 3 7 in 6 5 in 27 in³ 16 in³ 140 in³ 4 in 6 ft ft³ 19 ft³ 58 ft³ 9 ft 4 ft 8 65 cm³ 9,240 cm³ 4,620 cm³ 15 cm 28 cm 22 cm 9 57 in³ 3,000 in³ 6,000 in³ 12 in 25 in 20 in 10 15,625 in³ 75 in³ 150 in³ 25 in Lindsay Perro

14 Week three Circles & Cylinders Area & Circumference Formula Sheet Circles & Cylinders Notes Practice Worksheets

15 Guided Practice: Answer Key 1. Find the volume of the cylinder below. 8 cm Step 1: Find the area of the base. 20 cm cm² Step 2: Multiply the area of the base by the height. 4,019.2 cm³ Step 3: Be sure to include units and an exponents in your answer. Volume is always written in cubic units because it is the product of three measurements. 2. Find the volume of a cylinder given the following measurements: Radius of base = 10 inches Height = 7 inches Step 1: Find the area of the base. 314 in² Step 2: Multiply the area of the base by the height. 2,198 in³ Step 3: Be sure to include units and an exponents in your answer. Volume is always written in cubic units because it is the product of three measurements Lindsay Perro

16 Independent Practice. Show your work! 1. Find the volume of the given cylinder. 7,065 cm³ Answer Key 40 cm 15 cm 2. Find the volume of a cylinder with the given measurements: Circumference = 8 in, Height = 4 in in³ 3. Find the volume of a cylinder with the given measurements: Radius = 14 ft, Height = 13 ft 8, ft³ 4. A cylinder has a radius of 8 feet and a height of 22 feet. Find the volume. 1, ft 5. Find the volume of a cylinder with a radius of 4.5 feet and a height of 15.5 feet ft³ 6. A cylinder has a circumference of 10 feet and a height of 7 feet. Find the volume ft³ 2011 Lindsay Perro

17 Name Answer Key Date Let s Eat Pi! Solve each problem. Find your answer in one of the two answer boxes. # Answer 1 Answer 2 For problems 1 4, find the area of the circle using the given information. 1 Radius = 8cm cm² cm² 2 Diameter = 18in in² 1, in² 3 Diameter = 6in in² in² 4 Radius = 10ft 78.5 ft² 314 ft² For problems 5 7, find the circumference of the circle using the given information. 5 Radius = 7cm cm cm 6 Diameter = 12in in in 7 Radius = 20in 62.8 in in For problems 8 10, find the volume of the cylinder using the given information. 8 Radius = 8m, Height = 9m m³ 1, m³ 9 Diameter = 22cm, Height = 15cm 5,699.1 cm³ 22,796.4 cm³ 10 Diameter = 14in, Height = 11in 1, in³ 6, in³ Lindsay Perro

18 Week four Pythagorean Theorem Pythagorean Theorem Notes Practice Worksheets

19 Name Answer Key Date Pythagorean Theorem Notes & Practice Notes What is the Pythagorean Theorem? o A way to determine whether or not a triangle is a right triangle, given the side measurements. o A way to determine the missing side length in a right triangle. What is the formula? o a² + b² = c² Where a and b are the lengths of the legs or shorter sides And c is the length of the hypotenuse or long side. Examples 1) Given a right triangle, if side a = 5 inches and side b = 8 inches, what is the measurement of side c? a) Step 1 Determine whether you are missing a short side or the long side. In this case we are missing the long side. b) Step 2 Substitute the given information into the formula. a² + b² = c² 5² + 8² = c² c) Step 3 Solve for the missing variable. 5² + 8² = c² = c² d) To undo a square we use a square root. 89 = c² 89 c 2) Given a right triangle, if side a = 6 inches and side c = 10 inches, what is the measurement of side b? a) Step 1 Determine whether you are missing a short side or the long side. In this case we are missing a short side. b) Step 2 Substitute the given information into the formula. a² + b² = c² 6² + b² = 10² = = c c) Step 3 Solve for the missing variable. 6² + b² = 10² 36 + b² = d) To undo a square we use a square root. b² = 64 b = b 64= 8 To undo a square, we use a square root. When you are missing a short side, it doesn t matter if you solve for a or b. Lindsay Perro

20 Guided Practice 1) Determine the missing side length in the given triangle. 7m 15m a) Step 1 Determine whether you are missing a short side or the long side. In this case we are missing the SHORT side. b) Step 2 Substitute the given information into the formula. a² + b² = c² 7² + b² = 15² c) Step 3 Solve for the missing variable. Remember, to undo a square 7² + b² = 15² we use a square root. b = 13.2 m 2) A tree is 30 feet tall and casts a shadow that is 45 feet long. How far is it from the end of the shadow to the top of the tree? a) Step 1 Determine whether you are missing a short side or the long side. (In word problems, it is often helpful to draw a picture!) In this case we are missing the LONG side. b) Step 2 Substitute the given information into the formula. a² + b² = c² 30² + 45² = c²? 30 ft 45 ft c) Step 3 Solve for the missing variable. 30² + 45² = c² 54.1 ft = c 3) A 14 foot ladder is leaning up against a 10 foot tall house. If the ladder is leaning at an angle, how far is the ladder from the bottom of the house? a) Step 1 Determine whether you are missing a short side or the long side. (In word problems, it is often helpful to draw a picture!) In this case we are missing the SHORT side. b) Step 2 Substitute the given information into the formula. a² + b² = c² 10² + b² = 14² c) Step 3 Solve for the missing variable. Remember, to undo a square we use a square root. Lindsay Perro 10² + b² = 14² b = 9.8 ft

21 Independent Practice Fill in the table with the length of the missing side. Round your answer to the nearest tenth. Show your work in the table below! 1. A = 3 in B = 4 in C = 5 in A = 6 m B = 12.6 m C = 14 m A = 12 cm B = 5 cm C= 13 cm A = 19.2 cm B = 16 cm C = 25 cm A = 7 mm B = 5.6 mm C = 9 mm Lindsay Perro

22 Independent Practice Continued 6. A television measures 16 inches tall and 20 inches across the screen. What is the measurement of the width of the television?? 12 inches 20 in 16 in 7. Your backyard is 22 feet long and 12 feet wide. How far is it from one corner of your back yard to the opposite corner? 22 feet 18.4 feet? 12 feet 8. The mall is 4 miles north of your house. The park is b miles east of your house. When you are at the park, you are 6 miles from the mall? How far is the park from your house? 4 miles 6 miles 4.47 miles? Lindsay Perro

23 Lindsay Perro Name _Answer Key Date Pythagorean Theorem Solve each problem. Find your answer in one of the two answer boxes. # Answer 1 Answer 2 For numbers 1 4 use the Pythagorean Theorem to determine whether or not the side lengths represent a right triangle. 1 a = 3 b = 4 c = 6 No Yes 2 a = 9 b = 12 c = 15 No Yes 3 a = 7 b = 24 c = 25 No Yes 4 a = 5 b = 12 c = 20 No Yes For numbers 5 10 use the Pythagorean Theorem to find the missing side length. 5 a = 4 b = b = 10 c = a = 4 b = a = 5 c = a = 11 c = b = 84 c =