1. The angle of elevation from point G on the ground to the top of a flagpole is 20. The height of the flagpole is 60feet. A 19.3 B 20.

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1 Geometry EO Review EO Sample Items Goal. The angle of elevation from point G on the ground to the top of a flagpole is. The height of the flagpole is 6feet.. -foot ladder is leaning against a wall. The foot of the ladder is feet from the base of the wall. What is the approximate measure of the angle the ladder forms with the ground? 9. Which equation could find the distance from point G to the base of the flagpole? sin sin x 6 6 x ladder is leaning against the side of a building. The ladder is feet long, and the angle between the ladder and the building is. bout how far is the foot of the ladder from the building? tan tan 6 x x 6.6 feet. feet. feet.9 feet. mountain climber stands on level ground m from the base of a cliff. The angle of elevation to the top of the cliff is. What is the approximate height of the cliff? m m m 66 m. Susan is making a small cone out of paper. The cone has a radius of. cm, and the angle between the lateral surface and the base is.6. The formula for the lateral area, s, of a cone is s = πrl, where r is the radius and l is the slant height. What is the cone s approximate lateral area? cm² cm² cm² cm²

2 Geometry EO Review EO Sample Items Goal 6. dead tree was struck by lightning, causing it to fall over at a point ft up from its base.. What is the approximate area of the trapezoid? If the fallen treetop forms a angle with the ground, about how tall was the tree originally? ft cm² cm² cm² 9 cm² 6 ft ft 6 ft 9. sign is shaped like an equilateral triangle.. n apple pie is cut into six equal slices as shown below. If the diameter of the pie is ten inches, what is the approximate arc length of one slice of pie? If one side of the sign is 6 inches, what is the approximate area of the sign? in²..6 in. 6 in.². in. 6 in.². in.,96 in.². in.

3 Geometry EO Review EO Sample Items Goal. n inflated round balloon with radius r = centimeters holds approximately,6 cubic centimeters of air. When the balloon is contracted such that the radius is / the original size, what is the approximate volume of the partially deflated balloon?. What is the approximate area of the shaded region?.9 x cm. x cm. x cm. square units.9 x cm. square units 9. square units. What is the approximate distance between the points (, 9,,) and (9,, )? 96 units. square units. Marianna designed the logo shown for a computer software company., units,6 units 9, units. What is the ratio of the surface areas of two spheres with volumes of 6 cm and cm? : : 6 : 6 : If the diameter of the circle is cm, what is the approximate area of the shaded part of the logo?. cm. 6 cm cm cm

4 Geometry EO Review EO Sample Items Goal. point is randomly selected on XY. What is the probability that it will be closer to the midpoint of XY than to either X or Y?. cylinder with a height of 6 inches and a radius of inches is inside a rectangular prism, as shown below. point inside the rectangular prism will be chosen randomly. What is the probability that the point will also be inside the cylinder? 6. circle is inscribed in a square, as shown below..%.9%.%.6% If a point is randomly chosen inside the square, what is the approximate chance that the point lies outside the circle? %. cube with edges cm long is painted red. It is cut into smaller cubes with edges cm long that are placed into a bag. One small cube is pulled out of the bag without looking. What is the probability of pulling out a cube with three of its faces painted red? % % 9%

5 Geometry EO Review EO Sample Items Goal 9. cube is painted as shown. The three faces that are not seen are not painted.. To win a carnival game, Keisha must throw a dart and hit one of circles in a dart board that is feet by feet. The diameter of each circle is inches If a point on the surface of the cube is randomly chosen, what is the probability that it will lie in the painted area? pproximately what is the probability that a randomly thrown dart that hits the board would also hit a circle? % 6% 6% %. If Jim threw a marble inside the circle, what is the probability that it would land inside the triangle? End of Goal....6

6 Geometry EO Review EO Sample Items Goal. The conditional statement all angles are acute angles is true. ased on this conditional statement, which of the following can be concluded from the additional statement the measure of is?. What is the contrapositive of the statement below? If a triangle is isosceles, then it has two congruent sides. The complement of is not an acute angle The supplement of is an acute angle. is an acute angle. If a triangle does not have two congruent sides, then it is not isosceles. If a triangle is isosceles, then it does not have two congruent sides. is not an acute angle. If a triangle has two congruent sides, then it is isosceles.. MNO is shown below. If a triangle is not isosceles, then it does not have two congruent sides.. Which statement is the inverse of the statement in the box? If a quadrilateral is a rectangle, then it is a parallelogram. Which statement about this triangle is true? m O mm m M mn m M mn m N mo If a quadrilateral is not a parallelogram, then it is not a rectangle. If a quadrilateral is a parallelogram, then it is a rectangle. If a quadrilateral is not a rectangle, then it is not a parallelogram. quadrilateral is a rectangle if and only if it is a parallelogram. 6

7 Geometry EO Review EO Sample Items Goal 6. Given: If there was lightning, then we did not swim. If there was lightning, then we did not jog.. Given: k m n Using either one or both of the given statements, which conclusion is valid? If we did not swim, then we did not jog. If we did not jog, then there was lightning. If we did swim, then we did not jog. If we did jog, then there was not lightning.. Given the statements: Which statement justifies the conclusion that? If k m n and are cut by transversal t, then alternate interior angles are congruent. If k m n and are cut by transversal t, then vertical angles are congruent. Linear pairs are supplementary. and are supplementary. Using either one or both of the given statements, which conclusion is valid? and form a linear pair. If k m n and are cut by transversal t, then alternate exterior angles are congruent. If k m n and are cut by transversal t, then corresponding angles are congruent. ngles that are not supplementary are not linear pairs. Supplementary angles are linear pairs.

8 Geometry EO Review EO Sample Items Goal 9. What is the inverse of the statement below? If a triangle is scalene, then no two angles are congruent.. Given RS TU, m (x ) and m (x ). If the triangle is not scalene, then there are two congruent angles. If two angles of a triangle are congruent, then the triangle is scalene. If there are two congruent angles in a triangle, then the triangle is not scalene. If the triangle is not scalene, then there are no congruent angles. What is m? º º º. In the diagram, GH IJ. º. Plane P contains points,, and. different plane, plane Q, contains points,, and. Which of the following represents the intersection of P and Q? If m GLK and m EFJ, what is m KEF? º 6º 6º º points,,, and

9 Geometry EO Review EO Sample Items Goal. XYZ shown below has a measure of (x + )º. The measure of is (x + )º and the measure of is (9x )º.. Given m RQS = (½ x + )º, m SQT = (¾ x -6)º m RQT x º. and What is the measure of 6 6 XYZ?. In the drawing, what is the measure of angle y? What is º º 9º 6º m RQS? 6. The measure of each exterior angle of a regular polygon is. How many sides does the polygon have? 9 6 9

10 Geometry EO Review EO Sample Items Goal. Given: m x m x m x º. º, º, and 9. If KLMN is a rhombus, and m KLM = º, what is the measure of? What is m? º º º 6º. regular octagon is inscribed in a circle. What is the degree measure of each arc joining the consecutive vertices? 9. is a parallelogram. If m 6x º and m x º what is the value of x?.. 6

11 Geometry EO Review EO Sample Items Goal. Given: is an isosceles trapezoid. M is the midpoint of. Prove: M M What is the missing statement and reason that completes the proof shown above? ; the legs of an isosceles trapezoid are congruent. M M; the base angles of an isosceles trapezoid are congruent. M M ; the corresponding parts of congruent triangles are congruent. ; if lines are parallel, interior angles on the same side of a transversal are supplementary.

12 Geometry EO Review EO Sample Items Goal.

13 Geometry EO Review EO Sample Items Goal. In a hexagon, three angles have the same measure. The measure of each of the congruent angles is twice the measure of the fourth angle and is half the measure of the fifth angle. The sixth angle measures. What is the measure of the smallest angle?. is the angle bisector of. Line a is parallel to line b. Line a is parallel to line c. Line a is perpendicular to line c. Line b is perpendicular to line c. 6. O bisects O. If m O = (x + 6)º and m O (x )º, what is m O? º 6º º If m m, what is m? º º º º º. For which type of convex polygon is the sum of the interior angles equal to the sum of the exterior angles, one at each vertex? triangle hexagon pentagon quadrilateral. In the figure below, is supplementary to under which of the following conditions?

14 Geometry EO Review EO Sample Items Goal. If m P, what is the sum of the measures of the remaining interior angles?. In XYZ, W is between Y and Z. The coordinates are X(, ), Y(, ), Z(, ), and W(, ). What is XW? altitude angle bisector median perpendicular bisector of the side º 6º 6º º. In rectangle, diagonal = (x 9) and diagonal = (x + ). What is? 6 9. Triangle MNO has coordinates M(, ), N(, ), and O(, ). What type of triangle is MNO? equilateral. In parallelogram RSTU, the diagonals intersect at E. If RE = and SU = 6, what is RT? isosceles right scalene 6

15 Geometry EO Review EO Sample Items Goal. It is given that and. y the reflexive property,.. is an isosceles triangle with = and median. The perimeter of is 6 units. Which reason could be used to prove? side-angle-side What is? hypotenuse-leg units side-side-side units angle-side-angle units units. is a trapezoid with median EF. What is the length of? 6. If the sides of a triangle are,, and x, which of the following best describes x? units units 9 units units x x x x

16 Geometry EO Review EO Sample Items Goal. In, X is the midpoint of and Y is the midpoint of. 9. triangle has interior angles that measure (x)º, (x + )º, and (x + )º. What is the measure of the largest exterior angle? º º º 6º If m 6 and m, What is m YX? 6º º 6º º. On a map, the points (, ), (, -), and (-, -) are located on the circular boundary of a town. Which point locates the center of the town? (, -) (, -) (, -) (-, ) 6. What is the most specific name for quadrilateral with vertices (, ), (, ), (6, ), and (, - )? parallelogram rectangle rhombus trapezoid 6. broadcast tower is located at point (-, ) on an xy-coordinate grid, where each unit is one mile. If its broadcast reaches only a -mile radius, what is the set of points where the broadcast is received by its listeners? ( x ) ( y ) ( x ) ( y ) ( x ) ( y ) ( x ) ( y ) 6

17 Geometry EO Review EO Sample Items Goal 6. In, Z is the midpoint of and Y is the midpoint of. 6. In JKLM, JK KL and JK ML. What is the area of the trapezoid? If YZ = and = (x ), what is x?. sq cm sq cm 6 sq cm 6 sq cm. 6. Which of the following statements is true? 6 6. In the circle below, what is the value of x? chord is contained in a tangent. chord is contained in a radius. chord is contained in a secant. chord is contained in an arc. 66. triangle has side lengths of cm, cm, and cm. Which side lengths form the largest angle? units 6 units units 9 units cm, cm cm, cm cm, cm cm, cm

18 Geometry EO Review EO Sample Items Goal 6. In circle O, the measure of arc = º and the measure of arc = º. 69. is a right triangle with altitude. What are the coordinates of point? (9, ) What is º º º 6º m E? (6, ) (, ) (, ). In order to create a pattern for a blanket, Ming needs to use two congruent circles as shown. 6. In the triangle, UW bisects XV. TX and UW are perpendicular to RV. If TX = ft and XV = ft, about how long is UV? If OP = in. and = in., what is the radius of one of the circles? in. ft. in. 6 ft 6. in. ft in. ft

19 Geometry EO Review EO Sample Items Goal. In circle O, which term correctly identifies XY?. gardener wants to enclose a circular garden with a square fence, as shown below. chord radius secant If the circumference of the circular garden is about feet, which of the following is the approximate length of fencing needed? tangent ft 6 ft. P is tangent to circle O at, circle O has a radius of 6 ft., circle P has a radius of ft., and = 6 ft. ft ft. The vertices of a hexagon are (6, ), (9, ), (6, -), (-, -), (-6, ), and (-, ). Which best describes the hexagon? What is? nonregular and convex nonregular and concave ft regular and convex ft regular and concave ft ft 9

20 Geometry EO Review EO Sample Items Goal. Jill wants to measure the width of a river. She marks distances as shown in the diagram.. Right SRU is shown below. What is the length of RS? Using this information, what is the approximate width of the river? 6.6 yards yards. yards yards 6 6. The exterior angle of a base angle in an isosceles triangle is. What is the measure of the vertex angle?. If PQRS is a rhombus, which statement must be true? 6 PSR is a right angle PR QS PQR QRS PQ QR

21 Geometry EO Review EO Sample Items Goal 9. In the picture below, what are the coordinates of P? (, 6, 6) (-6,, 6) (-6, 6, ) (6, -6, 6). regular octahedron has eight faces that are congruent equilateral triangles. How many edges does a regular octahedron have? 6

22 Geometry EO Review EO Sample Items Goal. spherical foam ball, inches in diameter, is used to make a tabletop decoration for a party. To make the decoration sit flat on the table, a horizontal slice is removed from the bottom of the ball, as shown below. If the radius of the flat surface formed by the cut is inches, what is the height of the decoration? in. 6 in. in. in.

23 Geometry EO Review EO Sample Items Goal. What is the approximate surface area of a regular tetrahedron with edge length cm?. Which of the following is a regular polyhedron? 66. sq cm. sq cm 9. sq cm 9. sq cm. Which of the following polyhedrons has exactly two congruent bases? dodecahedron prism pyramid tetrahedron. Two tetrahedra are congruent. One tetrahedron is glued to the other so that the glued faces of the two tetrahedra completely cover each other, producing a new polyhedron. How many faces does the new polyhedron have? The intersection of a sphere and a plane is a circle with a radius of cm. If the sphere has a radius of cm, how far is the plane from the center of the sphere?. cm. cm.9 cm 6. cm End Goal

24 Geometry EO Review EO Sample Items Goal. Point J (p, q) is a vertex of quadrilateral JKLM. What are the coordinates of J after JKLM is rotated about the origin? (-p, -q) (-p, q) (p, -q) (q, -p). GHI will be dilated by a scale factor of, resulting in GH I. What rule describes this transformation? (x, y ) = x, y (x, y ) = (x, y) (x, y ) = (x +, y + ) (x, y ) = (x, y ) 9. P Q R is the image produced after reflecting PQR across the y-axis. If vertex P has coordinates (s, t), what are the coordinates of P? 9. What is the rule for the transformation formed by a translation units to the left and units up followed by a 9 counterclockwise rotation? (x, y ) = (-y, -x) (x, y ) = (x, y + ) (x, y ) = [ (y + ), x ] (x, y ) = [ (y - ), x + ] 9. The point G(, -) is transformed according to the rule (x, y ) = (x +, y ). The image G of the transformation is then reflected over the line y = x, resulting in point G. What are the coordinates of G? (, ) (, -) (-, ) (-, ) (t, s) (s, t) ( s, t) ( s, t)

25 Geometry EO Review EO Sample Items Goal 9. G H I is the image of GHI after a transformation. Which choice describes the transformation shown? reflection over x-axis reflection over y-axis (x, y ) = (x, y) (x, y ) = (x, y )

26 Geometry EO Review EO Sample Items Goal 9. XYZ is dilated by a factor of ½. What is the ratio of the area of XYZ to the area of its image, X Y Z? 9. In the coordinate plane, right triangle XYZ is reflected over the line y = x. : : : : What are the coordinates of the vertex of the right angle in X Y Z? (, ) (, ) (, -) (, -) 6

27 Geometry EO Review EO Sample Items Goal 9. EF is reflected across the line y = x. Which matrix multiplication shows how to find E F?

28 Geometry EO Review EO Sample Items Goal 96. Which matrix calculation was used to transform STU to S T U?

29 Geometry EO Review EO Sample Items Goal 9 9. Triangle MRT has vertices at M(, ), R(, -), and T(-, -). If the triangle is to be translated by the rule (x, y ) = (x +, y ), which matrix expression models the translation? 9. GHJ with vertex matrix 6 is dilated by a factor of. In the image G H J, what are the coordinates of the vertex that lies in the second quadrant?,,, (, )

30 Geometry EO Review EO Sample Items Goal 99. The vertices of quadrilateral GHIJ are G(-, -), H(, -), I(, ), and J(-, ). G H I J is the image produced by translating quadrilateral GHIJ 6 units to the left. Which matrix represents G H I J? 9. M N O is the image of MNO produced by a translation units left and unit up. The vertex matrix for O N M is 6. Which is the vertex matrix for MNO? 9 6

31 Geometry EO Review EO Sample Items Goal. Polygon FGHI is represented by vertex matrix M. M = Which multiplication would be used to reflect polygon FGHI across the x-axis? End Goal