Geometry Questions

GK is tangent to circle O at point Q QR is the circle s diameter Find m GQR R O G e K

Refer to OJ for problems 9 11 Segment KL is tangent to OJ A M L If the radius is 3 and LM 2 what is KL Answer

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

AGHI circumscribes OK What is the perimeter of A GHI 5 in G K 2 in 6 in H

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

Lines I and m are parallel lines cut by the transversal line t Which THREE angles are congruent to 5 x A 41 x B x 28 C 22 4x D 1 2 3 4 5 6 7 8 24 m

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

3 Use the parallelogram to complete the stateme E G F 20 in 3 The measure of ZF a 40 b 50 D 40 A 10 in c 140 d 150 zoom in 3 O A B Oc D

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

6 Examine the parallelogram HIJK below H I 9x 1 K 7x 71 zoom in Determine which of the following values are correct Select three that apply a x 2 b x 4 C m l 35 d m ZH 145 e m j 150 f m 2K 34 6 0 0 0 0 0

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

3 3 2 The surface area of the rectangular container pictured is 216 square feet What is the value of x 216 10 feet

Find the value of the variables For the circle the dot represents the center 50 b Answer 39 a Input answer as a b c

Find the value of the variables Lines that appear to be tangent are tangent b a 224 Input answer as a b

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

Determine whether the equation represents y as a function of x x y2 49

7 Solve the rational equation remember for solving you want to get rid fractions 7 points 2 x 4 4 X 4 12 x 16

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

Formula Bank X2 Midpoint x x y 2 2 Distance x x Y Name of Property being verified Slope m Y2 Y X2 X Work to support the property

5 Find the perimeter of ADEF 19 J 16 40 E

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

0 420 28 0 2 0 48 3 Monica has 12 different flavors of coffee and is selecting which one she will drink each morning before work How many different ways can Monica choose a group of 5 flavors so that has a different flavor each day

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

3 73 8 42 Z YZ X 63 52 Y

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

Find the value of x to the nearest tenth 14 X Answer 18

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

Find the value of x 12 Answer 01

The circles below are congruent Which conclusion can you draw B R Select one O a BD RT O b ZCED ZSUT O c ZAEBZQUR O d CD ST

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

The circle below represents Earth The radius of the Earth is about 6400 km Find the distance d that a person can see on a clear day from height habove Earth Round your answer to the nearest whole kilometer h 20 km r d

In the circle what is the value of x X 8 Answer 12

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

The top of a table is in the shape of a circle that has a radius of 40 ine Which measure is closest to the area of the top of this table A 63 sq in OB 314 sq in OC 1 257 sq in OD 5 027 sq in

Find the value of each variable in the circle to the right The dot represents the center of the circle a Simplify your answer Do not include the degree symbol in your answer

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

Simplify the expression to a polynomial in standard form 2x 1 x 6x 7

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

Find the value of a The dot represents the center of the circle 74