Ext 6-8 Sampler

47 Grade8 Lines,Angles,Area, andVolume 36 ©Math Teachers Press, Inc., Reproduction by anymeans is strictly prohibited. True or false? (Note: means congruent or the same size.) _____ 3. CPA BPD . _____ 4. CPB and BPD are vertical. _____ 5. APD and DPB are supplementary. _____ 6. APD DPB . _____ 7. CPB and BPD are adjacent. _____ 8. CPB APD . Fill in themissingmeasurements or angles. Parallel LinesCut by aTransversal A line intersecting two or more lines is called a transversal. In this figure, parallel lines L andM are intersected by a transversal line P. Four pairs of vertical angles are formed. Can you name them?_______________, ______________ ___________________, ____________________ Use tracing paper to copy 4.Compare the copied angle to 6. How do they compare? ________________________________________ What 3 angles have the samemeasure as 4? ________________________________________ What 3 angles have the samemeasure as 1? ________________________________________ L M P 1 2 4 3 5 6 8 7 1. 2. 1 2 4 3 5 6 8 7 120° 1 2 4 3 5 6 8 7 Two parallel lines are cut by a transversal. 2 = _____ 5 + 6 = _____ 3 = _____ 5 + 7 = _____ 4 = _____ 7 + 8 = _____ 5 = _____ 1 = ____ = ____ = ____ 6 = _____ 2 = ____ = ____ = ____ 7 = _____ 8 = _____ Two parallel lines are cut by a transversal. 1 and _____ are vertical angles. 1 and _____ are supplementary angles. 1 = ____ = ____ = ____ 2 = ____ = ____ = ____ • C • P • A • D • B 42 ©Math Teachers Press, Inc., Reproduction by anymeans is strictly prohibited. Find the area.Write the formula. Substitute and solve. Area of aTriangle andParallelogram Kari cut off a corner and placed it on the other side to complete a 4 3 rectangle. Area of rectangle = length width = 3 • 4 = 12 Area of parallelogram = base height = 3 • 4 = 12 Formula: Area = bh Kari, John, and Xi’s groupwere asked to find the area of the parallelogram shaded on graph paper. John ismaking 2 flags from a rectangular piece of fabric. height base 3 cm 4 cm 3 cm 4 cm A = bh = • 3 • 4 =6 sq. cm 1. A = _______ (formula) A = _______ (substitute) A = _______ sq. cm 2. A = _______ (formula) A = _______ (substitute) A = _______ sq. in. 3. A = _______ (formula) A = _______ (substitute) A = _______ sq. ft. 4. A = _______ (formula) = _______ (substitute) = _______ sq. units 5. A = _______ (formula) = _______ (substitute) = _______ sq. units 6. A = _______ (formula) = _______ (substitute) = _______ sq. units 8 cm 11 cm 6" 13 " 8' 5' 5 6 8 5 .5 1.2 A triangular sail has a base of 8 ft. and a height of 10 ft. Howmany square feet of sailcloth are needed tomake the sail? A 18 B 36 C 40 D 80 10 ft. 8 ft. The triangle is the area of the rectangle. 37 ©Math Teachers Press, Inc., Reproduction by anymeans is strictly prohibited. MissingAngle in aTriangle The sum of the angles of any triangle is themagic number, 180°. If you know two angles of a triangle, you can find the third angle. A C Find themeasure of the third anglewithout using a protractor. 1. __________ 2. __________ 3. __________ 4. __________ 5. __________ 6. __________ ? 55° 90° ? 60° 60° 80° 50° ? 50° 80° ? 7. 45°, 75°, ________ 10. 65°, 75°, ________ 8. 36°, 84°, ________ 11. 42°, 42°, ________ 9. 90°, 45°, ________ 12. 35°, 110°, ________ 13. The angles in an equilateral triangle are congruent.What is themeasure of each angle? _________________ 14. One angle of a right trianglemeasures 62°.What are themeasures of the other two angles? _____________ _____________ 48° 32° ? 135° ? 15° A + B = 105° C = 75° A + B + C = 180° Themeasures of two angles in a triangle are given. Find themissing angle. 60° 45° + 75° 180° 180° – 105° 75° 60° 45° ? B All 3 anglesmust add up to 180°. Two of the angles add to 105°. What is themissing angle? Subtract the sum of the two angles from 180°. Check your answer. 44 ©Math Teachers Press, Inc., Reproduction by anymeans is strictly prohibited. To find the volume of a rectangular solid, find the number of cubes in one layer andmultiply that number by the number of layers. Volume = length width height = 4 3 2 = 24 cubic units height = 2 width = 3 length = 4 A cube is a special kind of rectangular solid inwhich the edges are all the same. Formula: V = e e e = 4 4 4 = 64 cubic units edge = 4 edge = 4 edge = 4 Volume of aRectangular Solid or Cube Write the formula, substitute and solve to find the volume of each solid. 1. V = _____ (formula) V =_____ (substitute) V =_____cubic units 2. V = _____ (formula) V =_____ (substitute) V = _____ cm 3 3. V = _____ (formula) V =_____ (substitute) V = _____ cm 3 4. l = 6.8 in., w = 4.2 in., h = 3 in. 5. l = 3 ft., w = 2 ft., h = 4 ft. 6. e = 1.3 cm 4 units (length) 3 units (width) 2 units (height) 10 cm 3 cm 7 cm 10 cm 10 cm 10 cm Follow four steps (sketch, formula, substitute, solve) to find the volume. 7. A schoolroom is 32 ft. long, 25 ft. wide and 12 ft. high. Howmany cubic ft. of air are in the room? ___________ 9. Each of three dimensions of a cubical bin are 6 feet. Find the volume of the bin. ___________ 8. A swimming pool 70 ft. long and 30 ft. wide is filled to a depth of 5 ft. Howmany cubic ft. of water are used? ___________ 10. A cube has a volume of 27 cu. cm. What is the length of each edge? ___________ 36 42 37 44 Scaffoldedpagesprovide the conceptual understandingneeded for increasingly abstract objectives.