2D Geometry Questions and Answers

8pts Using Figure below calculate the length of x and 2x Round your answers to the nearest hundredth 3 2x 5 X Figure 3 X 2x

Can you show that this quadrilateral is a parallelogram

Write the function in the form f x x k q x r x for the given value of k Use a graphing utility to demonstrate that f k r Value of k Function Rx 15x 10x 15x2 9 k 3

C oint Retake question A 3 B Chord CB is a diameter and B is 16 What is the measure of arc AB Your Answer Answer

Graph Sy z 1 y 2x 2 5 4 3 2 1 Clear All Draw 4 3 C 2 7 N my bo LAX 3 5

3 7 Directions Solve the following problems Make sure to show all of your work Find BE and AB Find SR if QS bisects ZPOR Find x in trapezoid ABCD B BE AB Q B 10 SR 8 E 6 6 D 4 15 E 15 12 20 S 9 9 2 points 2 points 2 po

Opening Activity Solve by Square Roots 2 10x 2 282

Solve by Quadratic Formula 2x 3x 10

3 In the diagram below AL BK CH DG If DG 3 GE 5 HG 5 KH 5 LK 5 determine the lef of AL BK and CH B D

Show all of your work for full credit 1 A lighthouse casts a shadow of 24 ft and a sailor standing at a distance of 18 ft from the base of t lighthouse If the sailor is is 5 5 ft determine the height of the lighthouse to the nearest foot

Use your knowledge of Inscribed angles to find the missing arcs and angles of the following Explain the process you applied to calculate the missing value 1 2 80 3 M J 55 Knowing these are central angles find the value of EACH angle and ARC Justify your reasoning for calculating each value mCFD mZMIJ L A K W 4 42 E 135 81 B V C D

and MJ 16 4 In the diagram below LM 19 6 LN 24 5 9 Find the length of NK Round your answer to the nearest tenth if necessary In the diagram below LM 19 6 LN 24 5 and MJ 16 4 Find the length of NK Round your answer to the nearest tenth if necessary

Question 3 1 point F E G Your Answer D If E 82 and D is 63 what is the measure of arc FED

0 S P R e Not drawn to scale If PQ 13 and OP 5 QR 8 find the length of SR Round your answer to one decimal place Your Answer

M N P MQN is 27 and arc OP is 136 What is the measure of arc MPO Your Answer

Question 7 1 point W Y Your Answer If mVX 85 find m Y X Answer

ion 8 1 point B Your Answer E C If BE 10 ED 12 and EC 4 what is the length of AE A

E Fu Your Answer H Given mGH 56 degrees and mEF 95 Find m J Answer G

Question 2 1 point G H If m GHI 54 degrees what is the measure of J Your Answer

1 A streetlight casts a shadow of 27 feet long If a garbage can 18 feet away is 3 feet tall and has a shadow that meets the shadow of the streetlight how tall is the streetlight A complete and annotated diagram is needed for full credit

Determine m CB 151 C E B D 34 A

The point A is outside a circle with center M The line between A and C intersects the circle at B and C and the line between A and E meets the circle at points D and E Given that mZCME 130 and m BMD 56 find mZA Answer

n the given figure find m AC m BD D B 1129 C A

3 Secants 10 Find the measure of the missing angle 95 7 261 Xo 53 208 1 po CLindsay Bowden 2017

Find x A x C 151 B

ABCDE is the regular pentagon drawn inside the circle M AX is a tangent to the circle at A and EX is a tangent to the circle at E Find mZAXE E X D M A C B

80 O 40 260 to 5 Solve for x 260 CLimbay Bouden 2017

Which question type did you feel most comfortable with Choose all that apply Central angles Inscribed Angles Tangent Angles Secant Angles Chord Angles

360 O 143 217 31 12 Find the m DE F D 939 1240 E CLindsay Bowde

2 Inscribed Angle 158 090 39 5 O 360 E 6 Find the m DEF D 79 1 pc Lindsay Bonden 2017

Find the value of x 75 P 100 x 30 Find the given measures in each parallelogram M 70 70 N Jack m ZM mZN D 50 2x 7 E 15 C 70 B DC AC

P 14 Prove similarity Complete the proof that AGHJ AGIH 1 G 2 3 4 5 H I Statement GH L HJ HI L GJ ZGHJ LGIH LG LG AGHJ NAGIH Reason Given Given

P 14 Prove similarity statements ETX ZW and ZVXW are supplementary Complete the proof that AVXY AUWY W X Y V U Statement 1 W and ZVXW are supplementary 2 ZY ZY 3 m2VXY m2VXW 180 4 m2W mzVXW 180 5 m VXY mzVXW m2W m VXW 6 m VXY m W Reason Given Definition of supplementary angles Transitive Property of Equality

13 Graph the following polynomials using the end behavior and behavior near an x intercept f x x 2 2x 3

14 Graph the following polynomials using the end behavior and behavior near an x intercept g x x 2 2x 3

Here is one part of a regular n sided polygon inscribed in a circle of radius 1 Come up with a general formula for the perimeter of the polygon in terms of n Explain or show your reasoning 1 1 eeble sho

onder Practicing Perimeter What do you notice What do you wonder C woro nisic103

nawas standard position 45 Show that cost 45 cos 45 The point Sovel lies on the terminal side af 45 in the point sardy lies on the terminal side of JON ja

MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the reference angle 8 for the special angle 8 8 255 0 Sketch 8 in standard position and label y B 8 8 0 X X A 8 X X

Information is given about A ABC Determine if the information gives one triangle two triangles or no triangle Solve the resulting triangle s Round the lengths of the sides and measures of the angles to 1 decimal place if necessary a 135 5 b 106 2 B 13 4 Select one O a One triangle A 17 2 C 149 4 c 233 3 b No triangle c One triangle A 162 8 C 3 8 b 30 4 O d Two triangles A 17 2 C 149 4 c 233 3 and A 162 8 C 3 8 c 30 4

1 point Let OABC be a parallelogram on the xy plane where O 0 0 A 2 7 and C 3 2 Find the angle between the diagonals of OABC arccos 0 5948430054102947 rad Answer

Q3 In the diagram 3 cm 2 cm P 4 cm ABC ACD and APD are right angled triangles AB 4 cm BC 3 cm CD 2 cm Work out the length of DP Diagram NOT accurately drawn

1 8 490 vitemos ng Figure 3 below solve for x esbri SSLESTA X Fic 7 K C X 110 xevio woled tenugi prial sigh L spist doos om

P14 Prove simi Complete the proof that AGHI AHFI G 1 2 3 H 4 F HI 1 GH FHL GI ZGHI LHFI 21 21 5 AGHI AHFI Statement I Reason Given Given

2 and ZQTU are supplementary Complete the proof that ASTU R S U T Q Statement 1 ZQ and ZQTU are supplementary 2 LS LS 3 m2STU m2QTU 180 4 m2Q mZQTU 180 5 m STU m2QTU m2Q m2QTU Reason Given Reflexive Property of Congruence Definition of supplementary angles ASQR

A rectangle a triangle and four congruent semicircles were used to form the figure shown 4 m 1231 10 m 6m Which measurement is closest to the area of the figure in square meters

The dimensions of a rectangular prism are given in the net below F 96 in 2 G 168 in H 222 in A J 444 in 7 in 3 in 9 in 3 in What is the total surface area of the rectangular prism in square inches 7 in

O 7 6 2 1 2 3 6 2 The graph above shows the base of an object Compute the value of the volume of the object given cross sections perpendicular to the base are squares Give an exact expression or round your answe least two decimals

4 Graph the following label all critical points and intercepts a y 3x 5 2 b y 2x 4 x 7 Hint This is a thinking problem not a plug in the numbers problem

4pts Using Figure 4 below solve for OB A 15 17 B C Figure 4 O MathBas com OB