2D Geometry Questions and Answers

Which statements can be used to describe a ray A Has only one endpoint B Has no dimension C Extends endlessly in both directions D A part of a line E Has two endpoints

Defined by distinct lines which intersect at right angles and at exactly one point A perpendicular lines B C D arc angle parallel lines

The diagram shown here represents A a line intersecting a plane in one point B C D two intersecting planes two intersecting lines contained in a plane two intersecting lines

In Exercises 3 and 4 find the values of x and y 4 3 to 46 16 80 y 20x 5y

Find GH 9 GH 51 I H Write your answer as an integer or as a decimal rounded to the nearest t

A right triangle has side lengths a b and c as shown below Use these lengths to find cosx sinx and tanx X C a b COSX sinx tanx 0 0

A right triangle has side lengths 9 40 and 41 as shown below Use these lengths to find tan M cos M and sin M 40 N L 9 41 SM tan M cos M 0 sin M

Starting with Triangle STR the Scalle Factor is Find all the lengths of the sides of Triangle GHF 16 ft S 12 ft T 8 ft R H

3 Given ZQ ZS are right angles 21 22 Prove QP SR Statement Q S are 4 P Reason right 4 s Given 3 S

Given ZQ S are right angles QP SR Prove 2324 P 4 S

5 Given SM PQ ment tical LS 20 SQ 1 PM Prove PN SN S P N M

In the triangle ABC side b 9 side c 9 and side a 10 what is the value of the cos A Round your answer to the nearest hundr picture of triangle is purely for labeling use angles and side lengths specified in the problem

In the triangle ABC side c 15 angle C 90 and angle B 53 what is the measure of side b 0 B picture of triangle is purely for labeling use angles and side lengths specified in the problem Type your answer

Solve for x Each figure is a trapezoid 11 M W 11 15 x 21 17 13 EC 20 FD 5x 10 51 T R X E 28 11 e 12 14 Find the length of the angle indicated for each trapezoid Z 11x 8 B 95 17 Find ZR 23 C 29 11x 2

17 19 Find the measure of the are or angle indicated 11 13 15 M B Y 88 72 59 30 C X Z L 12 14 16 18 20 2 30 T W L 73 63 69 R D 37 S M N

7 5 3 Assignment Date 11 22 Find the measure of the arc or central angle indicated Assume that lines which appear to be diameters are actual diameters 1 155 145 45 60 125 160 150 2 6 8 10 1 124 125 96 50 98 155 110 Period

assify each angle as right obtuse or ac

T 3 A man is walking his dog on level ground in a straight line with the dog s favorite tree The angle of elevation from the man s present position to the top of a nearby telephone pole is 30 The angle of elevation from the tree to the top of the telephone pole is 45 If the telephone pole is 40 feet tall how far is the man with the dog from the tree Express answer to the nearest tenth of a foot A 1 7 feet B 29 3 feet C 40 feet D 42 3 feet O A OB O C O D 30 45

14 Classify each angle as right obtuse or acute A

6 Write the ordered pair for the point J 5 K L A J 4 3 2 1 SH 5 4 3 2 1 2 3 F N 13 for Q X 5

B Write the ordered pair for the point H U P L N X D 2 B A 5

R M X S W FV Question 10 Type of dilation Englargement Reduction Question 11 IN O Congruence Transformation Scale Factor P 1 1

2 Use the figure at the right to name the point that is located at the ordered pair 2 1 U Y d N L 2 N G 6 3 H D To F B

4 Use the figure at the right to name the point that is located at the ordered pair 1 1 5 C U P L 4 3 2 N Z S G 5 4 3 2 2 X 34 5 H D F 2 3 4 T A B 5 X

1 Use the figure at the right to name the point that is located at the ordered pair 0 3 s C U A Lo N L 2 N G 3 2 2 3 4 5 H D F 2 T B W A

17 Give an approximate measure for the angle

16 Give an approximate measure for the angle R A

Scale Factor 3 Center 1 1 A B C B

a b C Draw this diagram Draw a perpendicular line from C to AB The perpendicular line meets AB at D Measure the length of AD A 8 cm 55 B 15 cm C

4 Evaluate the following 12 7 5 22 5 3 14 7 15 5 5 Divide the sum of 2 and 3 by their difference 17 34 6 During a festival sale the cost of an object is 870 on which 20 is off The same object is available at other shops for 975 with a discount of 6 Which is a better deal and by how much 7 Simplify 21 5 5 of 20 5 5 5 0 5 x 8 5

Circle O has center 5 5 and radius 4 Circle P has center 3 1 and radius 5 Which describes how Circle O can be transformed to show that Circle P is similar to circle O translation of Circle O x y x 2 y 6 dilation of the 4 image with center 3 1 and scale factor 3 translation of Circle O x y x 6 y 2 dilation of the 4 image with center 3 1 and scale factor 5 translation of Circle O x y x 2 y 6 dilation of the 5 image with center 3 1 and scale factor 4 O translation of Circle O x y x 6 y 2 dilation of the 5 image with center 3 1 and scale factor 4 None of the other answers are correct

Scale Factor Enter any fractions as decimals rounded to the tent place

R M Q X S twt Question 10 Type of dilation O Englargement Reduction IN

Find the linearization of the function z x y at the point 5 4 L x y

Use your work from 1 3 to determine the scale factor that maps any circle with radius r onto any circle congruent to circle with radius s k

In circle S m RTQ 47 Solve for x if mRQ 5x 32 If necessary round your answer to the nearest tenth

m x 200 n x 200 p x 200 q x 200 Graph B Graph C Graph D 37 200 150 100 50 K A B C D 2 3 1 Match each of the above equations with a graph Write the equation below and explain your reasoning for each choice Graph A Reason Reason Reason 5 Reason 6 7 80

Quadrilateral TUVW is shown SERE If TUVW is reflected along the y axis what would be the cooridinates of V type your answer 23 1 point The lengths of two sides of a triangle are 24 inches and 43 inches What is the range of possible lengths in inches for third side a of the triangle Answer x Answer 16 type your answer 19 20 18 82 30 33 5

3 OM F Function YES or NO Domain 2 Range y 100

A circle has a radius of 7 in Find the radian measure of the central angle 0 that intercepts an arc of length 15 in Do not round any intermediate computations and round your answer to the nearest tenth 8 radians X

Which is equal to sin 62 cos 14 sin 14 sin 28 cos 28

Which is equal to sin 65 cos 25 cos 65 sin 15 sin 75

Which is equal to cos 63 sin 27 cos 12 cos 27 sin 12

Find the cosine of ZW 77 67 X W 10 Write your answer in simplified rationalized form Do not rou cos W

21 Which equation represents the circle to the right a x 2 y 3 9 b x 2 y 3 3 c x 2 y 3 9 d x 3 y 2 9 30

Find the cosine of ZX Z 8 X 15 17 Simplify your answer and write it as a proper fraction improper fraction or whole r cos X

15 As cars drive up a ramp at a multi storey car park they go up 2 metres The length of the ramp is 10 metres Find the angle between the ramp and the horizontal 10 m 2 m

1 Use the table to the right What is the probability that a randomly chosen patient did not catch a cold given they exercised a 15 19 b 3 5 c 15 16 d 16 25 a 15 16 b 4 25 Exercised Did not exercise Totals c 3 5 Caught a cold 2 Using the above table What is the probability that a person chosen at random who exercises but did not catch a cold 8 10 18 d 19 25 Did not catch a cold 30 2 32 Totals 12 50

20 You drive from the Willis Tower to Toyota Park and then from Toyota Park to Wrigley Field and back to Willis Tower You know that the distance from Willis Tower to Wrigley Field is 10 miles what is the total distance of your trip Round to the nearest tenth Wrigley Field a 10 6 miles c 26 9 miles b 20 6 miles d 33 6 miles E H S E Toyota Park Willis

Point C is is 3 1 of the way from point A 4 2 to point B 8 6 What are the coordinates of C