Geometry Questions

Given the triangle below find tan 0 Enter the answer as a fraction Provide your answer below 3 4 5 0

9 O Answer Check Find the diameter of OO A line that appears to be tangent is tangent If your answer is not a whole number round to the nearest tenth 12 to the nearest tenth 24

S hat is mST nswer 100 hat is mZQPT swer A

You focus your camera on a circular fountain Your camera is at the vertex of the angle formed by tangents to the fountain You estimate that the angle is 46 What is the measure of the arc of the circular basin of the fountain that will be in the photograph The measure of the arc of the circular basin of the fountain that will be in the photograph is Simplify your answer HETO AME

APQR is inscribed in a circle with m P 70 m Q 80 and m R 30 What are the measures of PQ QR and PR Type integers or decimals

Find the value of the variable B

ngle Measures a C Question 6 12 4 17 Find the value of c using the given chord and secant lengths in the diagram shown to the right Round to the nearest tenth as needed Points 0 of 1 10 13

K What is the value of y y Type an integer or a decimal

Find the value of x X Type an integer or a decimal to

efer to OC for problems 1 3 Segment DE is tangent to OC D C F elect one DE 4 and CE 8 what is the radius E a 8 6 b 4 3 c 4 d 2 10 DE 8 and EF 4 what is the radius

A piece of cardboard is 2 9 times as long as it is wide It is to be made into a box with an open top by cutting 2 inch squares from each corner and folding up the sides Let x represent the width in inches of the original piece of cardboard Answer the following questions CIC K 2 2 2 2 a Represent the length of the original piece of cardboard in terms of x Length 2 9x in Use integers or decimals for any numbers in the pression b Give the restrictions on x What will be the dimensions of the bottom rectangular base of the box

122 Answer Check Input answer as a b c b 50 Variables For the circle the dot represents the center 39 2 Find the value of the variables For the circle the dot represents the center I a Input answer as a b c

10 i I 1 I I T 1 I 1 I I 1 1 i 1 I 1 I I T i I L I I T I I 1 1 I T I I 1 I 1 8 Find an 6 1 I I I I 1 I I I I 1 I I I I 1 I I I I 1 T I I 1 I I I I 1 I 1 4 2 14 p u I 1 12 1 1 18 1 10 1 16 1 1 1 i 1 1 i 1 4 1 1 6 I 1 2 i I 7 10 12 714 equation for the graph above D I 1 1 1 1 T 1 1 1 1 I 1 1 1 I I 1 1 T 1 I I T I I i 1 1 I 1 1 1 1 4 6 I 1 1 I I 1 1 1 I I I 1 1 I I I I 1 I 1 T i I 1 i 1 T I I 1 i 1 T I I 1 I I T 8 10

1 A student inscribes quadrilateral ABCD inside a circle The measures of angles A B and C are given below Find the measure of each angle of quadrilateral ABCD m A 8x 4 m B 5x 4 m C 7x 4 2 A student inscribes an angle inside a semicircle to form a triangle The measures of the angles that are not the vertex of the inscribed angle are x and 2x 9 Find the measures of all three angles of the triangle Explain how you got your answer

84 a Answer Check nput answer as a b c bo a 78 Co 42 Find the value of the variables For the circle the dot represents the center b 87 36 nput answer as a b c

Find the value of x to the nearest tenth X 4 2 10

Find the values of x and y Lines that appear to be tangent are tangent X Do not include the degree symbol in your answer JO 238

the value of x X ver eck 4 9 6 3 X the value of x to the nearest tenth 18

Find each indicated measure for circle O a mZA b mCE c m c d mZD e mZABE a mZA Do not include the degree symbol in your answer A 740

K Which arc does ZC intercept ZC intercepts EFC FCE CDE Question 1 12 3 1 EO F Points 0 of 1 C O D E 7 por

23 m 4 5x m 5 4 x 5 24 m 2 4x 3 m27 5 x 3 25 m 3 1 26 m 1 m25 x 52 II 35 3 5 6 7 8 4 N Exercises 23 30

D Exercises 17 18 18 Given Find AB DC DB bisects LADC m 1 36 m A

1 Similar polygons The quadrilaterals JKLM and PQRS are similar Find the length x of QR 0 Z M 2 8 X 9 8 S R S

16 Given Find M 43 65 MNL NO and Zs as shown x y and z R 26

1 m A 63 and m B 42 2 m B 39 and m C 820 3 mA m C 57 4 m B 42 and m A m C A Exercises 1 6 03 B

In Exercises 13 to 15 j k and AABC 13 Given m3 L 1 50 m 4 72 m 1 m2 and m25 Find m B A 5 6 3 4 Exercises 13 15 2 1 C

In Exercises 9 and 10 classify the triangle not shown by considering the measures of its angles 9 a All angles of ABC measure 60 b In ADEF mLD 40 and m E 50 10 a In AXYZ m X 123 b In ARST m R 45 m S 65 and m T 70

15 Given Find m 1 122 3 m 5 m22 m3 and m24 41 5

8 a In AXYZ XY YZ b In ARST RS 6 ST 7 and RT 1 8

houses at points R and T in front of the plane With angle measures as indicated find m R 12 000 37 65 R 37 On a map three Los Angeles suburbs are located at points N Newport Beach P Pomona and B Burbank With angle measures as indicated deter mine m N and m P 8 The roofline of a house shows the shape of right triangle ABC with m C 90 If the mea of C B 33 X 2x N

15 Does the relation is complementary to for angles have a reflexive property consider one angle A symmetric property consider two angles A transitive property consider three angles

angles 24 and 26 have been bisected Using intuition what appears to be true of 29 formed by the bisectors 10 Make a sketch to represent two planes that are a parallel b perpendicular 11 Suppose that r is parallel to s and m 2 87 Find a mZ3 c m 1 b m 6 d m27 12 In Euclidean geometry how many lines can be drawn through a point P not on a line l that are a parallel to line e b perpendicular to line 1 2 3 X4 9 56 7 8 1 2 3 4 5 6 7 8 t S 9 Find 19 Given Find 20 In the figure BE L BE par each ot with Ex

c transitive property consider coplanar lines m n and g 6 In a plane 1 m and t 1 m By appearance how are e and related

4 If m 4 110 8 find a m S b m 8 EY l 1 2 3 4 5 6 7 8

7 With respect to b as a transversal for lines a and c a which angle corresponds to Z2 b which angle is the alternate interior angle for Z6 8 With respect to c as a transversal for lines a and b a which angle 12 5 6 10 9X11 12 Exercises 7 8 3 7 8 corresponds to 25 b which angle is the alternate exterior angle for 4 a b

Properties are some of the rules of mathematics which allow you to manipulate values and equations Most students are able to use the properties but do not realize their name nor why or how they work Match each property to each situation 3 x 7 3x 21 If a 40 then 3 8 a 15 5 0 0 If y 100 then y 10 90 5 0 5 Choose Zero Product Property Zero Sum Property Subtraction Property of Equality Distributive Property Division Property of Equality Choose Choose Choose

15 m with transversal t and 00 bisects LMON If m 1 112 find the following a m 2 b m 4 c m 5 d m MOQ 16 Given Find 17 Given Find e m Transversal t m 1 4x 2 m 6 4x 2 x and m 5 m n Transversal k m 3 x 3x m 6 x and m 4 x 4 x 5 EY m l 6 3 LO 1 2 M 4 At 5 0 7 I Exercises 15 16 6 N

In Exercises 27 to 35 complete the formal proof of each theorem 27 If two angles are complementary to the same angle ther these angles are congruent Given Prove 21 is complementary to 23 22 is complementary to 23 21 42

Given Find Given Find m n Transversal k m 3 x 3x m 6 x and m 4 m n Transversal k m 1 m 2 m 8 x 4 x 5 5x y 3x y 3x 5y x y and m 8 m 2 1 4 n 3 Exercises 17 19 6 LO 5 8 7

3 If two angles are supplementary to the same angle then these angles are congruent Given 1 is supplementary to 22 23 is supplementary to 22 21 43 Prove HINT See Exercise 27 for help 2 3

In Exercises 19 to 26 use the drawing in which AC intersects DB at point O A 19 If m 1 125 find m2 m 3 and m 4 20 If m 2 47 find m 1 m 3 and m 4 21 If m 1 3x 10 and m 3 4x 30 find x and m 1 D 3 O 1 2 4 B C

19 Sometimes symbols and abbreviations are used in place of a word or phrase What word or phrase is represented or abbreviated by each of the following b Zs c supp d rt a I e m 1

In Exercises 1 to 6 state the hypothesis H and the conclusion C for each statement 1 If a line segment is bisected then each of the equal segments has half the length of the original segment

2 If there were no understood restriction to lines in a plane in Theorem 1 4 3 the theorem would be false Explain why the following statement is false In space there is exactly one line perpendicular to a given line at any point on the line

3 Does the relation is perpendicular to have a reflexive prop erty consider line A symmetric property consider lines and m A transitive property consider lines l m and n

Is the following equation linear and con x 13y 3 17

lows The length of a line segment equals the sum of the lengths of its parts State a general conclusion regarding AB based on the following figure

Define a function f that represents a bucket s height d above the water in feet in terms of the angle of rotation measured in radians from the 3 o clock position Then use your function to find a bucket s height above the water when the angle of rotation is 4 radians from the 3 o clock position

Find the equation of the the line satisfying the given conditions Through 2 3 perpendicular to a second line y x O y x Oy x Oy x O y x

Solve 5 sin 5x 4 for the two smallest positive solutions A and B with A B A B Give your answers accurate to at least two decimal places