2D Geometry Questions and Answers

8 Unit 9 Review Evaluate tan 225 Show all k

circumference of a circle with a radius of 27 feet

The slope of line I is and its y intercept is 3 1 2 What is the equation of the line perpendicular to line I that goes through 1 5 A y 2x 3 B y 2x 7 1 11 C y x 2 1 D y x 2 9 2

What is the value of y y Type an integer or a decimal

What is the value of x Type an integer or a decimal X

Find the value of c using the given chord and secant lengths in the diagram shown to the right C Round to the nearest tenth as needed C 10 12 19

Refer to OP for problems 4 8 given mQR 100 T P Answer S What is mST R

ft 14 ft 15 ft a Write the formula you re using b Determine the volume

DE is tangent to OC D C F Select one O a 8 6 O b 2 10 O c 4 O d 4 3 E If DE 4 and CE 8 what is the radius

EF is tangent to OD What is the value of x E 66 D G 7 F

If MN 5x 5 and NK 3x 1 determine which of the following values are correct Select two that apply zoom in a MK 20 b JL 10 C NK 10 d MN 20 e JL 30 M 2 Swlect ALL th A B C D

911XZ 5X 1 and PZ 3x 1 what is XP W 10 If WY XZ 38 what is PZ Refer to the figure in No 9 zoom in 9 10 Type a response Type a response

A soccer team has 10 players and needs to choose 2 captains How many ways can the captains be selected

7 Jessica draws two parallelograms One of the parallelograms is a square Which zoom in properties must Jessica s two parallelograms have in common Sel apply a Four right angles b The opposite sides are parallel c Diagonals are congruent d Opposite interior angles are congruent e Consecutive interior angles are complementary 7 A CA

8 What is the value of x in the parallelogram below E F 24 6X 6 D 44 42 G 2x 30 zoom in 8 Type a response

1 Which equation can be used to solve for the value of x 4x 5 11x 6 11x 4 9x 10 a 4x5 9x 10 90 11x 4 4x 5 b c 11x 4 11x 6 d 4x 5 11x 4 180 1 O A B C D

me ligure shows triangle ABC Select all expressions that must be equivalent to cos A A sin x OB sin y C cos y D cos 90 y E cos 90 A to yo 20

Find the value of a For the circle the dot represents the center 17 20

raph the solution set of the system 14 y 5x 1 x y 25 10

Parallelogram ABCD A 0 0 B 3 3 C 7 1 D 4 4

7 Verify the identity Remember to include rationale for each step tan 2x cos 2x 2 sin x cos x

10 Find the area of circle C by using the Law of Sines to find the radius Hint What kind of triangle ABC A C 100 35

7 In a survey about a change in public policy 100 people were asked if they favor the change oppose the change or have no opinion about the change Of the 100 people surveyed 40 are male and 28 oppose the change in policy Of the 28 who oppose the change 20 are female What is the probability that a randomly selected respondent to the survey is a man or opposes the change in policy

Topic Main Ideas Questions 45 45 90 Special Right Triangle 30 60 90 Special Right Triangle Notes Examples 1 long 8 4 long 7 7 Directions Find the value of each variable 2 3 y x 30 45 45 y 46 60 short X 2x X 2 y y 60 Leg 60 sitt Directions Find the value of each variable 5 5 3 10 Hypotenuse x 2 45 8 Class Period 30 x Shorter Leg Longer Leg 3 Hypotenuse 2x 60 L y y y 25 14 x X y 20 3 Note The legs of a 45 45 90 triangle are always congruent 6 19 9 45 y Note The shorter leg is always opposite the 30 angle and the longer leg is always opposite the 60 angle y vig 30 322x x 16 y 16 3 y 30 943

For problems 8 10 use the figure and information below ON and OO are congruent PQ is a chord of both circles 0 NO 12 in and PQ 8 in how long is the radius to the nearest tenth of an inch Answer

JG is the diameter of OM Which conclusion cannot be drawn from the diagram K N M L H G Select one O a KN NI O b LG GH O c GH GL O d JGL HL

The polygon circumscribes the circle What is the perimeter of the polyg 8 mm 7 mm 3 mm 17 mm

Assume that lines that appear to be tangent are tangent O is the center of the circle What is the valu 0 x 40

3 Find the Arc Length and Sector Area 10 points D Arc Length in terms of pi Sector Area round to nearest tenths 4 Answer the questions below 10 points Find the equation of a line that is parallel to x 2y 4 and I passes through the point 4 2 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

YOU DO ROUND 1 1 A fish tank in the shape of a rectangular prism has a base with dimensions of 40 inches by 50 inches allu height of 20 inches If the tank is filled with 20 water determine the volume of the water in the tank a Draw and label the fish tank b Which formula will you use c Volume of the fish tank V Bh lw h or V Bh bh h d Volume of the water in the fish tank

Rewrite the following polynomial in standard form x 100 1 5x x4

Find the value of each variable For the circle the dot represents the center 99 do 1100 910 60

20 Given BC CD AB BD Prove AB CD that A First show that BC CD and BC CD BD Then use 21 Given WY YX Blank 2 AB CD That means that AB CD Prove m ZWY mLYWX because m ZWY BOC Blank 3 Blank and 2CD BD Divide to show that CD mzZWY mZYWX by the Z W X Blank 4 Y D Proof Because WY YX mzWXY mzYWX because if one side of a triangle is Blank 1 longer than another side then the angle opposite the longer side has a the angle opposite the shorter side But Blank 2 m2WXY by the Exterior Angle Theorem Property to show Blank 3 So Blank 1 options addition subtraction substitution Blank 2 options BC CD BD CD CD BD Blank 3 options BC BD Blank 1 options Blank 2 options greater measure than measure that is less than Blank 3 options Blank 4 options Reflexive Symmetric niniu

1 Below are two uniquely shaped juice containers Determine which container can 5 cm 7 cm 2 cm 7 cm 6 cm

1 5 cm 3 cm 4 10 cm 4 cm a can of paint covers 6cm how many cans of paint would be needed to cover the prism in 1

YOU 2 The following glass is filled 25 of the way with water Determine the volume below 4 cm 2 cm

In OO mBD 150 and AB CD What is mCA A B

If mTL 116 and m ZWJ 102 find mZJ Answer m ZJ T L W J Z Submit Answer

2 Which of the figures below has a larger surface area 3cm 10 cm 5 cm 7 cm 2 cm

3 1 can of paint covers 100 cm In the cylinder r 8 cm and h 20 cm Determine paint cans needed to paint both objects 12 6 5 h

This Venn diagram shows sports played by 10 students Jada Gabby OA 3 0 50 OB B 0 375 3 8 O C 0 60 3 OD 0 10 PLAYS BASKETBALL 0 30 Fran lan Juan Let event A The student plays basketball Let event B The student plays soccer What is P AIB Ella Mai Karl PLAYS SOCCER Mickey Marcus

Find the coordinates of a point on a circle with radius 15 corresponding to an angle of 80 x y Round your answers to three decimal places

Question 1 Points 2 If the point 9 5 is translated 6 units left and 5 units up then find the translated coordinates of the point O 3 10 O 3 10 O 3 10 O 3 10

2 Graph h x x 3 1 Describe transformation

3 Find the volume of each solid Then list these solids in order from the one with the least volume to the one with the greatest volume Part I Give the volume of each solid Show your work A a cube with edge 5 cm B a cylinder with a radius of 4 cm and a height of 4 cm C a square pyramid with base edges 6 cm and height 6 cm D a cone with a radius 4 cm and height 9 cm E a rectangular prism with a 5 cm by 5 cm base and height 6 cm Part II list these solids in order from the one with the least volume to the one with the greatest volume

4 Three balls are packaged in a cylindrical container as shown below The balls just touch the top bottom and sides of the cylinder The diameter of each ball is 13 cm a What is the volume of the cylinder Explain your method for finding the volume b What is the total volume of the three balls Explain your method for finding the total volume c What percent of the volume

2 An ice cream vendor presses a sphere of frozen yogurt into a cone as shown below If the yogurt melts into the cone will the cone overflow Explain and show work Note The diameter of the scoop is 8 cm and the height of the cone is 8 cm 12 cm

3 Eric has a trolley He wants to use that trolley to transport wooden blocks The size of the trolley is 3 960 000 square centimeters He found the wooden blocks to have a density of 0 0029 blocks per square centimeter How many total wooden blocks can he carry in the trolley

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

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