Session+13+Supplement+v.2

Session+13+Supplement+v.2 - LESSON#13 Geometry 2 General...

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LESSON #13: Geometry 2 General Properties of Triangles: Recap! The longest side is opposite the largest angle, the shortest side is opposite the smallest angle, etc. Memorize These! P = x + y + z b × h 2 A = x y z a + b + c = 180 d = b + c (x – y) < z < (x + y) Equal angles imply equal opposite sides and vice-versa.
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LESSON #13: Geometry 2 General Properties of Triangles: Recap! c a b Pythagorean Theorem: a 2 + b 2 = c 2 Pythagorean Triples: 3 : 4 : 5 5 : 12 : 13 7 : 24 : 25 8 : 15 : 17 c a b 30 : 60 : 90 45 : 45 : 90 x : x 3 : 2x x : x : x 2
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LESSON #13: Geometry 2 Knewton Exclusive: Right Triangle/Rectangle Tips Any two of these five define a unique shape. In other words, given any two, you can solve for any of the others. b a c a b c 1. Side Length 1 2. Side Length 2 3. Diagonal/Hypotenuse 4. Perimeter 5. Area
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LESSON #13: Geometry 2 A = r 2 π C = 2 r or C = d π r d d = 2r π o b c a x x 360 Arc abc Circumference Area of sector abc Area of circle O = =
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LESSON #13: Geometry 2 General Polygon Features: Exercise In rectangle WXYZ, if a = 135°, what is the value of b + c ? 170 180 190 200 210 W X Y Z
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LESSON #13: Geometry 2 In the figure shown, what is the twice the value of u + v + w + x + y ? 180 270 360 540 1080 General Polygon Features: Challenge Exercise
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LESSON #13: Geometry 2 Quadrilaterals: Exercise W WXYZ is a parallelogram. The ratio of ZV to VY is 2:5. If the area of WXYV is 42, what is the area of WXYZ? 35 42 48 49 63 X Y Z V
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LESSON #13: Geometry 2 Quadrilaterals: Challenge Exercise If p is the perimeter of rectangle X , what is the value of p ? 1. Each diagonal of X has a length of 5. 2. The area of X is 12.
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LESSON #13: Geometry 2 Annulus : Exercise 3 4 7 16 9 16 1 4 1 3 A new type of coaster is made up of a circular piece of cork with a diameter of 12cm surrounded by a ring of wood with a thickness of 2 cm. What fraction of the coaster’s area is made up by the wooden ring?
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LESSON #13: Geometry 2 Cornelius is standing at the center of a circular jogging track with a diameter of 100m. He is planning to run to the track, run ¾ of a lap, and then run straight back to the center. If he can run 150m per minute, and t is the number of minutes it takes him to complete this run, then which of the following is true? 0.5 < t < 0.75 1.0 < t < 1.5 2.0 < t < 2.5 2.5 < t < 3.0 3.5 < t < 4.0 Circles, Arcs, Sectors: Exercise
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LESSON #13: Geometry 2 Central and Inscribed angles: Exercise If XZ is a diameter of this circle with center A, and triangle XYZ is isosceles, what is the length of arc XY ? X Y Z 1. The area of triangle XYZ is 98. 2. Arc XY and Arc YZ are equal. A
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LESSON #13: Geometry 2 Three-Dimensional Figures: Exercise 1 An oilcan in the shape of a right circular cylinder is ¼ full of oil. If the volume of oil in the container is 27 cubic inches, and the height of the container is 6 inches, what is the diameter of the base of the cylinder, in inches? 2 π 6 2 π 3 2 9 π 3 π 3 π
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LESSON #13: Geometry 2 1. Every book packed into the box has the same dimensions.
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