2D Geometry Questions and Answers

Determine if the following statements are true or false based on the definitions of the functions f x x and t x The graph of t x is a reflection of the graph of f x over the y axis The graph of t x is a translation of the graph of f x up by 2 units The graph of t x is a translation of the graph of f x left by 2 units t x has a vertical asymptote at x 1 x 2

A 06 O 12 09 O15 D 4x 9 15 B C Figure 2 Using Figure 2 above calculate the numeric value of x

OB Figure 1 Using Figure 1 name the segment that represents the Tangent AO O AB 12 O AC 8

5 Find the measure of angle one in each triangle Explain your reasoillg 35 M 1 65 35 180 m4l 100 180 106 100 M41 80 33 1 57 40 1 30

1 Find the measure of the missing angle Show all work for credit 65 V 57 2 Find the measure of the missing angle Show all work for credit 40 7 3 Find the value of x Show all work for credit 55 x 59 84 x 74 54 4 Find the measure of angle A Show all work for credit W x 51 5 Find the measure of angle A Show all work for credit

For 1 3 use the Exterior Angles Theorem to find the value of the variable Show all work for credit 1 2 3 61 79 30 70 65 Find the m JKM Find m J 6x 1 39 60 2x 5 126 FG 5x 17 M 4

7 In right triangle ABC mzC 90 If Sin A determine cos A cos B and si

8 In right triangle ACE mzC 90 and Tan A Determine the following trig ratios sin A E tan A tan E cos A cos E

6 In right AJKL above determine the m2J and m2K to the nearest tenth of a degl 22

In a right 4 triangle one angle measures x where What is cos 90 x sin x tin 5

the absolute maximum and minimum values of f on the set and D f x y x 3x y 12y 2 is quadrilateral whose vertices are 2 3 2 3 2 2 2 2 maximum minimum

2 Q If sin x cos y what must be true about x and y answer choices x y 90 x y x 2y 180

13 Choose the correct answer segment 2 013 2 015 2 014 2 014 indicates the minor arc intercepted arc major arc 2 016 2 017 2 018 2 019

3 Find the area of the sector 37 7 in 24 7 in 10 8 in 13 in 120 10 8 in 4 2 4 in 6 in

J O O 24 ft 9 6 ft 12 ft 5 ft 14 Find the length of the arc 12 ft 246

25 Find the area of the segment 24 7 in 11 7 in 50 7 in2 10 8 in 120 Sector of a circle 10 8 in 2 4 in 6 in The area of the sector is 37 7 in and the area of the triangle is 13 in

1 In triangle WXZ XY 15 YZ 25 WA 18 and AZ 32 Determine if WX AY W A Y X

2 Find x Bridgeview Southview Davis 15 24 8 Broad Main X

in a triangle LA eB C 180 know LA 45 0894 90 2A 135 0896 180 LA 180 180 135 089 LA 44 9106 244 91

Find the area of the composite figure Round your answers to the nearest tenth if necessay 10 cm 7 11 Ao 314 2 A 3 5 Pts Total Area apothem Perimeter

The two rectangles are similar Find k k 13 2 21

Nat and Brett are standing due east of a 138 m tall tower Nat s angle of elevation to the top of the tower is 18 Brett s angle of elevation to the top of the tower is 23 How far apart are Nat and Brett Round to two decimal places as needed Show your work here

Jean and Cathy are standing due east of a 160 ft tall tower Jean s angle of elevation to the top of the tower is 25 Cathy s angle of elevation to the top of the tower is 42 How far apart are Jean and Cathy Round to two decimal places as needed Show your work here

What is a solution to the equation 43 x 6 11 0

Use the information provided to write the equation of a circle Center 4 1 Radius 10 O O O x 2 y 3 100 x 1 y 4 4 x 4 y 1 100 x 4 y 1 4

What is the reason for 18 1 M is the midpoint of BC 2 AB DC 3 MB MC 4 ZB ZC 5 ZAMBZDMC 6 Statement AABM ADCM Reflexive Property ASA AAS Alternate Interior Angles Alternate Exterior Angles Corresponding Angles Definition of Midpoint Given M is the midpoint of BC AB DC Prove AABM ADCM 1 Given 2 Given 3 Answer to 17 4 Answer to 18 Reason 5 Vertical angles are congruent 6 Answer to 19

28 What are the values of x and y in parallelogram ABCD O A B C OD A x 30 y 40 B x 30 y 60 C x 40 y 60 x 40 y 45 D E x 40 y 30 D A 3x 120 C 2yo

MNOP is a square Solve for x M d O x 3 5x 8 O x 10 5 Ox 11 O x 21 75 199 DE CRIST THIRTY INTER BEDEN DEN WARENESSE P N 3x 14 O 761 DELHE ton verkappiestom RUS con la que you PORT PRESE ME DOLA PASIRI BIRG

An oblique prism has a base area of 3x square units 13 5 What expression represents the volume of the prism in cubic units 36x 24x 39x 15x

A solid right pyramid has a square base with an edge length of x cm and a height of y cm X Which expression represents the volume of the pyramid x y m x y cm xy cm O1 xy cm

3 A man is standing 20 feet away from a tree The height of the tree is 25 feet If he is looking up at the tree what is the angle of elevation formed to the nearest tenth

YOU DO ROUND 1 1 An observer in the top of the lighthouse looks out to a boat in the water If the distance from the top of the lighthouse to the boat is 55 ft and the height of the lighthouse is 40 ft determine the following Label the angle of depression as x B Mae Box com b Determine the angle of depression to the nearest tenth of a degree C c Determine the distance from the base of the lighthouse to the boat

Given ZA ZB mzA 55 and mzB 5x 10 Prove x 9 Statement 1 ZA ZB 2 m A m B 3 mzA 55 4 55 mzB 5 m B 5x 10 6 55 5x 10 7 45 5x 8 x 9 Reason 1 Given 2 Congruency 3 Given 4 Substitution 5 Given 6 Substitution 7 8 Division Property of Equality Select the reason that best supports Statement 7 in the given proof A Distributive Property B Subtraction Property of Equality C Substitution D Division Property of Equality

w alt 3 C D 5 ask 1 7 3 A Fishy Situation in aquarium manager drew a blueprint for a cylindrical fish tank The tank has a ertical tube in the middle in which visitors can stand and view the fish 3 ft 2 ft shi Question 2 If not how many fish should be added or removed 4 ft The best average density for the species of fish that will go in the tank is 16 fish per 100 gallons of water This provides enough room for the fish to swim while making s that there are plenty of fish for people to see The aquarium has 275 fish available to put in the tank Question 1 Is this the right number of fish for the tank

Which angle has a cosine of B 8 OLA OZB 20 10 6 of A cosine of 3 5

24 20 16 12 8 4 Ol 2 4 6 8 10 12 14 16 18 A 16 B 17 C 18 D 19 X The scatterplot shows the relationship between two variables x and y A line of best fit is also shown A x 6 what is the y value predicted by the line of best fit

Given Triangle ABC has angle measures of mzA 3x 8 mzB 3x and mzC 3x 10 Prove mzC 64 Statement 1 ABC is a triangle 1 Given 2 mzA mzB mzC 180 2 Triangle Angle 3 mzA 3x 8 4 mzB 3x 5 mzC 3x 10 7 9x 18 180 8 9x 162 Theorem 9 x 18 10 mzC 3 18 10 11 mzC 64 3 Given Reason 4 Given 5 Given 6 3x 8 3x 3x 10 180 6 Substitution 7 Algebra 8 Subtraction Property of Equality 9 2 10 11 Algebra

2 A f t C f t The table shows several values of time t in seconds and a rocket s corresponding propulsive force f t in millions of newtons The rocket launches at t 0 seconds Which graph could represent the relationship between t and f t O50SOnoso5 45 50 45 40 35 30 25 20 15 10 5 0 1 2 3 4 5 6 40 35 30 25 20 15 Time Propulsive force seconds in millions of newtons 0 10 0 1 2 4 17 5 1 IND 11 TUL 47 38 31 47 22 1 2 3 4 5 6 B f t 4 50 45 40 35 30 25 20 15 10 5 to 0 50 CHOSOSOSOS D f t 45 40 35 30 25 20 15 10 1 2 3 4 5 6 Nt 5 TH 10 14 H 130 S5 t 1 2 3 4 5 6 t

3 In right triangle XYZ mLX 90 and tan Y Find the va Sin Y Can Y Sin Z Cos Z

a In right triangle ABC determine the following trigonometric ratios sin C cos C tan C sin A cos A nA noen angle Gard dream c b What observations do you have from the ratios above 8 10 B 6 D

8 In right triangle LMN m M 90 and Tan L 3 Determine the ratios below Tan N Me ding from class Sin L Sin N

1 Which of the following is true in a right triangle a cos 90 B cos B b sin 90 B sin B c tan 90 B tan B d cos 90 B sin B Explain your answer using the key understanding from class

Determine how if possible the triangles can be proved similar OA SAS OB SSS OC AA O D Not Similar 8 15 10 16 24 12 8

ind the volume of the oblique pyramid with a square base 21 16 0

DIRECTIONS Select all correct answers Given ASUN and ADAY S U N D A Y Which two relationships would prove ASUN ADAY by Side Angle Si SAS Similarity Theorem SU UN SU SN SN UN

AOPQ AABC What is the y coordinate of B if the coordinate of A is 0 0 and the coordinates for C is 12 0 y P 2 3 0 0 0 Q 4 0 X

Find the volume of the triangular pyramid given the measures shown Show your work here 2 9 6

Which postulate or theorem can be used to prove the two triangles congruent B O A ABAT AMAN because ASA OB ABAT AMAN because AAS O C ABAT AMAN because SAS O D ABAT AMAN because HL M A N

Which of the following triangles is similar to APQR O A O C 21 V 17 5 15 18 O B O D 10 4 12 15

Oblique triangular prism has a base area of 25 square units me of 275 cubic units What is the height of the prism ow your work here