t~ ~ G.9: The student will verify characteristics of quadrilaterals and use properties of quadrilaterals

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1 ,/ 11 c. j'../ Strand: Polygons and Circles..f1 t~ ~ G.9: The student will verify characteristics of quadrilaterals and use properties of quadrilaterals J to solve realworld problems. ~ ";\Jhich quadrilaterals have... (f? 1. four right angles?~' Soy 8. perpendiculardiagonals?s\~t ~UJ), ~ SQ. rfl 2. exactly one pair of parallel sides? ~ \::cs 9. opposite angles congruent?'f \' '\ S \. \, ~ «3. two pair of opposite sides congruent? T~ ~, \ \ R 10. diagonals bisect each other?~ \ <;: ~, 4. four congruent sides? S<i.. \ Yo~~\..U:) 11. four congruent angles? ~~ \ ~"\... C. 1C5. two pair of opposite sides par~lel? 12. four congruent sides and four congruent d;; 6. no sides congruent? 'b~~~ P &j 7. two pair of adjacent sides congruent} but not angles? SC\ ~CLf\..9 D (' :~ sides congruent? V~ tjl~~ ~ JJ,_=, J1 '\)"t)~t S l' ~~ s "1 "'~S 3 8. Using your knowledge of quadrilaterals, investigate the types of symmetry (point symmetry, line symmetry, or no symmetry) the quadrilaterals shown above might have. Justrfy your answers. Point symmetry: When a figure can be mapped onto itself by a rotation of 180. Line symmetry: When a figure can be mapped onto itself by a reflection over a line. G.10: The student will solve realworld problems invol.ving angles of polygons; This figure is composed of a regular pentagon and a rectangle. e B 54'" D los" What is the measure of each of the angles dentified as x?

2 12 G.11: The student will use angles, arcs, chords, tangents, and secants to a) investigate, verify and apply properties of circles; b) solve realworld problems involving properties of circles; Point A represents a vertex of an equilateral'triangle inscribed in circle O., Which other point is also a vertex of this equilateral triangle? ~ A Point V n drcle 0, mfg :;::: 30, mile.:::: 120, and L1 ~ /...K. B PointX ' C Point r E::in,Z) \~o~ l\s~ ~ ~t) ~ \'\CJX '/... ::. SO F~"'" 30 0 ~ J K G J What is mef? B 40" C '15" n circle 0, mlsot:= 68, {) W\\e&,S ~ L S\\\? ~..=it

3 13 c) find arc lengths and areas of sectors in circles. Given: Three concentric circles with the center () Which s dosest to the area ofthe shaded region? KL~ LN~ NO ~ A 231 sq in. KP =42 inches " sq in. Given: Circle Twith WP =36 centimeters K \', ~~\f l\l\\\\ _ 4<4\1 L.. d:1b t.'" 4C1 "T\ \, \.S (~,\4 =s ~~ S ) 50 w.. T l30 () p c~ Find Which best represents the area of the shaded sector? C;; 11~~ c;i),_, B 1801T cm 1 \.~. C 23411' em] '_' ' cm l the arc length of the arc outlined by the shaded region.

4 G.12: The student, given the coordinates of the center of a circle and a point on the circle, will write the equation of the circle. Circle 0 is defined by the equation x 2 + b' 2)2 = 25. Plot the center of cirde 0 and one point with integral coordinates that lies on circle O. (b\l) 'r~s )' i /'! 8,,/ L 6 '. 5 '1 4 ~ i'r 1+ f. +t j 3 1,..., 1...,.!.. 1 t \ i i ' ll..( 3 2 1v / \ /!.~ v! :: s t '6 _. ' H f1,. 1. f '7 if',..._. 1.~' f g F' f 1_. 9, x 14 Given: Circle 0 with diameter CD C( 7, 4) and D(l, 2) Create the equation of this circle. The Equation of the Circle ll0 +~\'~~~~.:1 ][J Given: Circle V W( 4,6) Radius;:: 10 units Which point lies on circle V? A (0,4).~ C',s U) \,\.X'\~ B (2, 10) S~" ~ ';r..~ CO~~~ ~~ '.' 0 (6, 16) ~ je. " ,.,,_..~..~..'.,...,..,..;. '1',... V / P 1/ " r~ i(' ' 1 1 v :>./ '. J f i ". ",/ 'v

5 G.13: The student will use formulas for surface area and volume of threedimensional objects. to solve realworld problems. A cylinde! has a volume.of 300".cubic centim~ters and a base with a circumference of C:::: ~'" 10rr centimeters. What S the height of the cylinder? '1 ' '" = \\'( 15 \0n ;;J l' r ' A 30 em : 0]. :.1\la~ ~. =ru.0 B 15 em ~,,~ S ~ "(,...' C 12 em.~: 0 3 em 2~ rwo cylinders, a sphere, and a cone are shown. Select the two objects with the same volume. j. 6cm., Cylinder 2: s:, :=. ~'("'1.+~ :. ~ 1'\ ~ ~'tf 'll.l\"rr 'l~ \~\r ~ 'L. ~ 4L\~OtsTl\ Examples: Find the area of the following regular polygons: J3 S'1. 4 qj3 s=3cm ~ :LottJ'rt\ \~ ll\l '\ s =4 m

6 16 G.14: The student will use similar geometric objects in two or threedimensions to a) compare ratios between side lengths, perimeter, areas, and volumes; The ratio of the volume of two spheres is 8:27. What is the ratio of the lengths of the radii of these two spheres? 3ft: ~JJ, ~ b) determine how changes in one or more dimensions of an object affect area and/or volume of the object; f the height of a rectangular prism is decreased by!, then which statement s true? 3 d'\\p _ ~~3. '_' A The volume would decreas V=\w 3 ~ \~ 1. _ B The volume would decrease by l. \j~ \\J\/~ ~ 31 6?.L.\4 C The volume would decrease by l, 9 _ 0 The volume Vlould decrease by c) determine how changes in area and/or volume of an object affect one or more dimensions. of the object; The heights of two similar triangles are n the ratio 2:5. f the area of the larger triangle is 400 square units, what is the area of the smaller triangle? esquareun;) \... B 160 square units '. ' x ~~S ~~S 4 Ts ~(1) C 1,000 square units \\ooo= ~X 'X ;.. o 4c:s~ 2,500 squar'e units For the rectangle, find d) solve realworld problems about similar geometric objects. the value of x. A company makes two similar cylindrical containers. The total surface area of the smaller container is 0.81 times that of the larger container. The height of the larger container is 60 centimeters. What is the height of the smaller container? ~ 8 B 'W.o em C 24.3 em '. D 21 cm

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