2D Geometry Questions and Answers

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

Consider rectangle EFGH H E G F Prove segment EG is congruent to segment HF T II

Greg ties a 5 rope to the top of a 4 pole in his yard and draws a diagram to help determine the angle made between the rope and the ground O sin 5 Rope Which equation can Greg use to find the value of x 3 5 O cos 45 4 5 x 4 pole O tan x 4 O sin r 5 4 O tos x 5

Consider polygon ABCD shown below B c E A G F D Select all the ways that describe rigid transformations that take AEFD to CFEB Reflect AEFD across line EF Rotate AEFD 180 degrees counterclockwise around point G Rotate AEFD 180 degrees clockwise around point G O Translate AEFD by the directed line segment from F to E and then reflect across line FE Translate AEFD by the directed line segment from F to E and then rotate 180 degrees clockw around point E

10 The translation x y x 10 y 6 is applied to AABC to create a new image M B C Graph AA B C on the coordinate plane C 10 9 6 9 11 ARST is reflected across the line y x to form ARST Find the coordinates of the points R S and T

12 Quadrilateral ABCD has vertices A 1 2 B 1 3 C 4 3 and D 4 2 It s dilated by a factor of 2 with the center of dilation at the origin What are the coordinates of the resulting quadrilateral A B C D 13 Determine the measure of x in the figure below 58 80

Given sin 4 in Quadrant 2 find sin 24 10 13 100 169 20 69 169 10 26 89 169

Solve problems involving the of a circle central angle circumference Solve problems involving Words to Know Write the letter of the definition next to the matching word as you work through the lesson You may use the glossary to help you arc length radian Define measure A a standard unit of measure for angles the measure of a central angle that subtends an arc that is equal in length to the radius of the circle B an angle whose vertex is at the center of a circle and whose sides are radii of that circle BOK C a portion of the circumference of a circle MAGNE AMOR ARRICANE D the distance around a circle

Circumference of a Circle The circumference of any circle or the distance around the circle can be determined using either of these formulas 2 m r radius C md d Applying Circumference The London Eye is a Ferris wheel that at its highest point stands 135 meters tall The diameter of the London Eye is 120 meters A person rides the wheel two full revolutions How far has the person traveled Calculate the circumference Use the button on your calculator C nd C C 377 m Find the distance in two full revolutions 377 2 F O m

Arc Length Arc length s is a c 2 C C 10m Use 3 14 as an approximation for this is of the whole circle 4 For any arc length s of the circumference of a circle S SA S A circle has 360 This arc has a central angle of 90 That means that 8 360 2 r 31 4 A where 8 is the central angle and r is the radius of the circle O 90 5 S B