2D Geometry Questions and Answers

1 In the diagram below a circle is inscribed in a square Find the

5 Solve for the value of x K J 83 M L

2 Quadrilateral ABCD is inscribed in circle O as shown below If m A y 30 and m2D x 10 which statement is true 1 x 85 and y 50 x 90 and y 45 x 110 and y 75 x 115 and y 70 A 80 x 10 8 75

10 I In circle A below which of the following is not true EF is a chord b CB is a tangent line BA is a diameter a C d AD is a radius II In circle A which of the following is true Select all that apply a DE is a radius b CB is a tangent line BA is a diameter C d AD is a radius B A LL F

9 Find the area of the shaded sector 49x 6 175x m 2 30 m 11

In the diagram below of circle X shaded region in terms of 18 in and ma N Y 75 18 in X

1 What is the arc length of BC a 1 9 in b 1 2 in c 1 0 in

Find the surface area of each cone in terms of 5 4 10 m 2 m 12 m 4 cm 5 m 3 cm 16 m 5 m 1 2 Find the lateral area of each regular pyramid to the nearest tenth 7 7 m 8 7 m 27 7 m 2 cm 40 cm Find the surface area of each regular pyramid to the nearest tenth 10 11 5 cm 20 cm 9 cm 2 cm 5 cm 30 m 9 cm 6 9 8 ft 15 ft 12 6 ft 21 ft 12 ft 15 in 24 in 12 ft 12 ft 12 ft

Electricity Gas Water 15 kwh 1 100 ft3 03 10 Gal Phone Internet Maintenance Joe lives in an apartment and uses 200 kwh of electricity 800 ft of gas 400 gallons of water and internet and phone plans as described in the table He pays no maintenance costs because he rents the apartment Calculate his monthly utility bill A 299 20 B 190 00 Utilities C 179 20 D 449 20 40 month 100 month 120 month

Find all solutions to the equation 2 cos 0 Write your answer in radians in terms of a and use the or button as necessary Example x 2ka k Zorx ka kez Help with this notation 0 0 8 0 0 X R krkez

Find an equation of the parabola with vertex 3 3 and focus 3 9 1 2 9 0 0 S X

3 Determine the values of 0 if 0 0 360 given that sin 0 Use special triangles to determine the related acute angle 2 2

Solve for measure of angle a 55 25 a a If 2 secant lines intersect outside a circle a b Enter

5 You are playing an arcade game In this game lights go round and round on the outside of the circle The probability that you stop the light in arc A or arc D is equal to the probability you stop the light arc C or arc B Using this information is E the center of the circle 20 E D 90

Question 5 of 6 Submit Test Oo Describe a sequence of transformations that take trapezoid ABCD to TSCU You may use the draw tool to help illustrate your thinking box B 22 23 Geometry Final Part 1 C

Zircle 3 BD and CD are tangent to Circle A ED and DG are tangent to Circle F Prove AABD is similar to AFGD Please make a flowchart proof A O F

7 Find the volume and surface area of 34 3 cm 6 cm

4 AABD is similar to AFGD BD and CD are tangent to Circle A ED and DG are tangent to Circle F Given that AD 57 956 in EF 3 in and we know the angles marked on the diagram find the length of BD You may use the fact that AABD AACD and AFGD AFED However if you use this fact or the fact that AABD AFGD please state that you are using it Also find the scale factor 2 A B C 2x 10 12x 15 D 6x E G F

Find the value of y 148 y y 1 V

In the figure AB BC and CE DE BAG 30 CBD 46 DCE 40 and EFG 32 ACF 30 F 32 B 88 46 E 40 D

D In the figure ABCD is a trapezium and EF is a straight BCF 154 and EAD 102 Find ZADC E 102 4 B 154 F

Find the point at which the line intersects the given plane x 44t y 5t z 1 t x 2y z 8 x y z

Provide the missing reasons for the proof Given LC LE Prove AABC ADBE A B W D E

Triangle ABC is similar to triangle FGH Given the following angle measures find the missing angle measures m A 22 degrees m B 75 degrees Enter your answers as numbers only m F degrees A m H degrees A A m G A degrees m C degrees

U W S X T R In the figure triangle UVW is similar to triangle RST VU 48 VW 22 and SR 24 What is the value of x Show all your work

Two polygons are similar if and only if there is a correspondence among their angles and among their sides so that all corresponding angles are congruent and all corresponding are proportional

Which of the following postulates and theorems can be used to prove triangle similarity AA SSS HL ASA

Find the APPROXIMATE Length of each arc Round your answers to the nearest tenth 11 6 9 yd

Arc Length and Sector Area Find the EXACT area of each sector 14 9 in 300

Find the slope of the line If an answer is undefined enter UNDEFINED y 5x 9

T F 2x 4 5 C 1 E 6 Line Segments about Circles D Find the measure of the line segment indicated

Circles Solve for x 11 19 8 9 X

15 Find DE F 10 9 E x 5 D G 8 T about Circles Find the measure of t line segme

Circles Find the measure of the line segment indicated 13 Find TU 7 W C 5 8x

ve for x Assume that lines which appear tangent are tangent 18 60 48

Circles Solve for x 12 6 5 X 7

17 Find m2SQR 79x 1 0 R 100x S

Find the measure of the arc or angle indicated 5 J K 80 L

Find the measure of the arc or angle indicated 7 32

3 Directions Find the length of each bolded arc Round to the nearest hundredth 1 2 4 If TR 11 ft find the length of PS P 7 5 in 35 S T R 16 6 If YV 28 in find the length of VYX 117 12 W X 15 118 4 cm 52 5 If MK 10 m find the length of MKL M 148 F E 7 If AF 23 cm find the length of EC 57 D 26 m 87

The center of a circle has the coordinates 3 2 Write the equation of the circle if a point on the circle ha the coordinates 1 2 Use the graph below if that helps you visualize the situation 4 2 6 S B 2 4 P 6 2 4 6 2

Find the measurement of arc XY N Y R 73 X 126

Find the central angle ZLBM and inscribed angle ZLGM for the circle if arc ML 44 ZLBM ZLGM G B M L

3 Find the value of a and b D R a 110 75 b C B a b

Triangle XYZ is a right triangle with ZQ L XY X a Z b Q Drag and drop a correct answer into each box to complete the proof of the Pythagorean theorem By the angle angle similarity postulate AYXZ AYZQ and AYXZ A ZXQ Sirke similar triangles b sides and Solving the equation for a and b gives a cf Adding those together gives of 2 12 a of co Factoring o

Tina plans to make wooden frames to put her two triangular art pieces in How much wood would she need fortriangle DFG Enter your answer in the box in 5 in A B 7 in 6 in C 15 in D 427 F 18 in G

Which theorem or postulate proves that A ABC and A DEF are similar O SAS Similarity Theorem SSS Similarity Theorem O AA Similarity Postulate 3 B A 7 6 C E 18 D 36 42

Use the figure for Questions 3 and 4 3 What is m42 A 50 B 70 4 What is m24 F 10 G 60 C 110 H 100 D 120 J 120 70 40

Consider the following figure ABDC with diagonal BC Sides AB and DC are congruent angle A is congruent to angle D and sides AC and DB are congruent B A C D Select all statements that are true O Triangles ABC and DCB are congruent by the Angle Angle Triangle Congruence Theorem O Triangles ABC and BCD are congruent by the Angle Side Angle Triangle Congruence Theorem Triangles ABC and BCD are congruent by the Side Side Side Triangle Congruence Theorem O Triangles ABC and DCB are congruent by the Side Angle Side Triangle Congruence Theorem O Triangles ABC and DCB are congruent by the Side Side Side Triangle Congruence Theorem

Line m is represented by the equation y 1 represent lines perpendicular to line m 0 y 3x 1 3 O y 2 Oy 1 2 3 O y 1 x 5 2 3x 1 0 y 2 2 1 Oy y 3 3 2 x 1 Select all equations that 3