Geometry Questions

3 Abigail is putting juice into cone shaped containers to make popsicles She has approximately one quarter of a gallon or 58 cubic inches of juice to make the popsicles with Each container has a height of 3 inches Use the information to complete the table indicating the maximum number of popsicles that Abigail could make with 58 cubic inches of juice Radius of the Maximum Container Number of Popsicles 0 5 inch 1 inch 1 5 inch

4 The volumes of two similar figures are 216 cm and 1728 cm The surface area of the larger figure is 864 cm Find the surface area of t smaller figure

3 The surface areas of two similar figures are 96 in and 216 in The volume of the larger is 216 in Find the volume of the smaller figure

4 The plane region is revolved completely about the y axis to sweep out a solid of revolution The solid formed is a cone Find the volume of the cone Show your work AY 10

4 Use the formula SA ph 2B to find the surface area of the rectangular prism below Show your work 4 8 ft 2 2 ft 1 9 ft

2 The Pyramid of Khufu is a square pyramid which had a side length of about 230 m and a height of about 147 m when it was completed The Pyramid of Khafre had a side length of about 215 m and a height of about 144 m when it was completed What was the approximate difference in the volume of the two pyramids upon completion

2 An artist creates a right prism whose bases are regular pentagons He wants to paint the lateral surfaces of the prism One can of paint can cover 30 square feet How many cans of paint must he buy if the height of the prism is 15 ft and the length of each side of the pentagon is 5 ft Show your work

4 6 Given Point is the midpoint of AC Point C is the midpoint of AD Prove 4AB AD Arrange the steps in order to complete the proof 1 2 3 4 G 5 Use the figure to complete the proof of the theorem 1 21 22 2 21 and 22 form a linear pair 3 21 and 22 are supplementary 4 21 and 22 are right angles If two congruent angles form a linear pair then they are right angles Given 21 22 Prove m 1 Given 2 3 4 Blank 2 Point is the midpoint of AC Point C is the midpoint of AD Given AABAD Addition AB AB AD 4 ABAD Substitution CD Definition of midpoint AC CD AD Segment Addition Postulate it is given that Z21 22 Also 2123 because these are ABBC AC All 4 BC AC AB AB AC AC AC AD Substitution Blank 1 options corresponding vertical angles Therefore 22 23 by the Transitive Property of Congruence by the Blank 1 2 OPTIONS Linear pairs are suppl Oliven If 2s are and suppl then they are right s Blank 2 options Converse of Corresponding Angles Theorem Converse of Alternate Exterior Angles Theorem that m

3 A box measures 10 in wide 12 in high and 14 in deep If all surfaces are made of cardboard how much cardboard is used to make the box Show your work

1 For a d use the diagram below 4 cm 4 cm 4 cm 4 cm 4 cm 4 cm 9 cm a Classify the prism b Find the lateral area of the prism c The bases are regular hexagons They are of each is about 41 6 cm Find the sum of their d Find the surface area of the prism

5 Serena is drawing pictures of cross sections of the right circular cone below Which drawing cannot be a cross section of the cone 1 2 3 4

Question 10 Points 1 Which of the following transformations carry the given regular polygon onto itself O Translation O Reflection O Dilation O None of the choices

2 Given that AJKL AGKH solve for x K G 4 6 X H L

Question 9 Points 1 Which of the following transformation carry the given regular polygon onto itself Rotation of 72 Reflection across the line of symmetry Rotation of 45 None of the above

6 Draw and name the vertical and horizontal cross section for the cylinder below Vertical cross section drawing and name

Question 5 Points 2 Identify the symmetry O Reflection symmetry O Rotational symmetry Both

3 Determine the surface area of the sphere below with a radius of 5 Express you 5

sson Posttest Points 2 Question 6 Which of the following transformations carry this regular polygon onto itself O rotation of 60 clockwise Orotation of 45 clockwise Orotation of 75 clockwise the line symmetry

Lesson Question 8 Points 2 How many lines of symmetry does a regular octagon have O 4 O 8 O 6

Lesson Posttest Question 3 How many lines of symmetry does the isosceles triangle have O 3 02 O 4 Points 1 O 1

Question 2 What is the order of rotational symmetry for a regular heptagon seven sided regular figure 07 O 5 Points 1 O6

1 In the diagram below a cylinder with a height of 8 yds and a radius of 13 yds 13 yd Determine the surface area a In terms of T the nearest tenth 8 yd

Lesson Posttest Question 1 Points 1 Polygon is a segments joined together closed line O open line O closed curved open curved Polygon onto plane figure made up of

t A gallon of paint will cover approximately 450 square feet An artist wants to paint all the outside surfaces of a cube measuring 12 feet on each edge What is the least number of gallons of paint he must buy to paint the cube 1 1 2 2 3 3 4 4

5 6 7 8 3 1 4 2 In the given picture there are transversal What is the relationship between angles 2 and 6 vertical supplementary corresponding alternate interior alternate exterior Which angle is alternate exterior to angle 8 Just ente the number If angle 5 has a measure of 140 degrees what is the measure of angle 3 CO

n Postte Points 2 Question 2 A point D 3 2 is rotated clockwise through 90 Find the new coordinates of D O D 2 3 O D 2 3 OD 2 3 OD 2 3

n Posttest Question 8 Points 1 Which of the following shows the coordinates of Q 3 5 after a translation of 3 units right O Q 0 5 O Q 6 5 O Q 6 2 O Q 3 2

Question 9 Which of the following shows the coordinates of C if the given rectangle is translated 2 units upward 8 7 6 5 Y 0 D A Y Points 1 2 O 4 3 3 O 3 4 O 4 5 6 5 C B 4 5 6 7 8 X

Question 3 Points 1 Which of the following shows the translation of K 3 2 two units down OK 3 2 OK 2 3 OK 3 0 OK 3 2

Question 5 Points 2 Which of the following transformations creates a figure that is similar but not congruent to the original figure O Reflection O Translation O Rotation O Dilation

Question 1 Points 3 The vertices of the triangle are A 3 5 B 6 1 and C 5 9 is dilated using a scale factor 2 Find the coordinates of the dilated triangle O A 5 7 B 8 3 and C 7 11 O A 6 10 B 12 2 and C 10 18 O A 1 3 B 4 1 and C 3 7 O A 6 10 B 12 2 and C 10 18

This table shows how many sophomores and juniors attended two school events A student is selected randomly from this group O A 0 51 OB 0 60 C 0 40 Sophomore Junior Total D 0 26 Jazz band Volleyball concert game 35 42 36 71 24 66 What is the probability that the student attended the jazz concert given that the student is a junior Round your answer to two decimal places Total 77 60 137

7 Prove that the quadrilateral whose vertices are the points A 1 1 B 3 4 C 1 5 and D 3 2 is a parallelogram X

5 Given ABCD is a parallelogram Prove 4ABD 4CDB D A C B

Which statement is not always true about a parallelogram a The diagonals are congruent b The opposite sides are congruent c The opposite angles are congruent d The opposite sides are parallel

4 Find the length of TS T 2x 15 S R x 15 U

1 The following polygon is a parallelogram Find the value of x 2x 20 3x 10

2 The following polygon is a parallelogram Find the value of x 8X 6 98

3 Find the mZKSO In the diagram below of parallelogram ROCK m C is 70 and m ROS is 65 TTT R O 65 LYSO3 S C 70 K

Two chords intersect at a point inside a circle that is not the center of the circle Which statement must be true O The measures of each pair of opposite arcs sum to 180 O Each angle measure is equal to the measure of the arc it intercepts O The sum of the measures of each pair of vertical angles is equal to the sum of the measures of the intercepted arcs O Each arc measure is equal to one half the sum of the vertical angles that intercept the arc

0 S R 94 T U In circle Y what is mTU 82 O 100 O 106 O 118

Frolls thoushds 9 A bag contains 2 red marbles 7 blue marbles and 8 green marbles If two marbles are drawn out of the bag replacing the first marble before drawing the second marble what is the exact probability that both marbles drawn will be blue 10 A bag contains 8 red marbles 3 blue marbles and 7 green marbles If three marbles are drawn out of the bag what is the probability to the nearest 1000th that all three marbles drawn will be red 11 A bag contains green and yellow color tiles You pick two tiles at random without replacing the fir one The probability that the first tile is yellow is The probability of drawing two yellow tiles is

1 61 16 With replacement 1 Suppose you draw two tennis balls at random from a bag containing 7 pink 4 white 3 yellow and 2 green tennis balls What is the probability of getting yellow replacing the ball and then getting pink Totalt 7 4 3 2 16 Plyellow 3 0 188 16 Unol P pink 7 6 438 16 Without replacement 3 Suppose you draw two tennis balls at random from a bag containing 7 pink 4 white 3 yellow and 2 green tennis balls What is the probability of getting yellow and then green P vellow the Pink 0 188 0 938 0 082 P yellow 0188 P green 7 5 0 133 Mixed Practice 5 A bag contains 6 red marbles 4 blue marbles and 8 green marbles If three marbles are drawn out of the bag what is the probability to the nearest 10th of a percent that all three marbles drawn will be green roubles 6 4 8 18 0 165 0 133 0 025 First Green 1 8 2 A bag contains red and blue marbles You pick 3 marbles at random replacing each marble between picks What is the probability that the last marble you choose is blue if there are 9 red marbles and 6 blue marbles Second 77 our Total marbles 9 6 15 P last is blue 0 4 15 4 A bag contains red and blue marbles You pick 2 marbles at random placing them in a box What is the probability that you get two red marbles if there are 10 red marbles and 8 blue marbles marbles 10 5 1 P first d 10 0 556 18 P secondared 9 0 529 PETRed 0 55610 529 0 294 17 6 What is the probability that you choose a Queen and then a King when choosing two cards from a deck Round your answer to the nearest thousandths place Cards 52 3 2 52 King is 2 1 queen is 0 006

U T Line segment ST is congruent to which line segment O SK O KU O UT OTK

In circle O AE and FC are diameters Arc ED measures 17 A B C What is the measure of EFC O 107 O 180 253 O 270

rea Volume 2 Calculate the area and perimeter 10 points HA and the volume and surface area of the solid below 10 point Perimeter Surface Area Period Geometry Final Exam Ope

Triangle BCD is isosceles and BC BD B A 100 What is the measure of BC O 100 O 120 O 130 O 160

F R to 50 H In the diagram of circle R mZFGH is 50 What is mFEH O 130 O 230 260 310 O O

A circular table top has a radius of 24 inches What is the area of the table top to the nearest square inch Use 3 14 for T O 75 in O 151 in O 1809 in O 7235 in

dar Unen 3 Find the equation of x 2y 4 and passes t ver the ques 5 Find the equation of a line that has a y intercept of 2 and it is perpendicular to a line that passes through the points 2 5 and 1 4