2D Geometry Questions and Answers

Macmillan Learning The mil is a type of angle measure used in the military This term is derived from milliradian and 1000 mils equal 1 radian What is the degree measure of 1 mil Use decimal notation Give your answer to three decimal places Include the degree symbol in the answer 1 mil A target is 1 yard wide and subtends an angle of 1 mil in a soldier s field of vision How far from the soldier is the target Suggestion Think of the target as an arc of a circle yards between the soldier and the target How many mils are there in a circle Use decimal notation Give your answer two decimal places

O Macmillan Learning Convert an angle of radian measure 6 to degree measure Give an exact answer Include the degree symbol in answer 67 radians

A right triangle has legs of length 4 and 16 Use the Pythagorean theorem to find the length of the hypotenuse Express numbers in exact form Use symbolic notation and fractions where needed length of hypotenuse

Macmillan Learning Recall that in a triangle the angle sum is r radians or 180 An equilateral triangle has all three angles equal What is the degree measure of an angle of an equilateral triangle Give an exact answer Use symbolic notation and fractions where needed Include the degree symbol in your answer angle

The graph of f x 2 13x 54x 72 is given below Use the graph of f to solve the following equation r 13x 54x 72 0 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 8 9 2 3 7 8

Prob 1 3 General Addition Rule Set backpound Clear fame Complete each probability model by finding the probability of B only Warm up Shade the region that represents the union on the two events A or B Then momote tha nenhahility A 0 25 B A 0 05 B

Show how each vertex of AEFG maps to its image Describe in words how to map AEFG to its image AE F G using a reflection 6 V G 4 R A fu Ay 10 8 6 4 2 2 4 6 101 Complete the table with the coordinates of the image points E F and G AEFG 4 5 2 5 3 2 E F G Type ordered pairs E F G AE F G

3 4 Angles 4 5 and 6 are in the ratio 2 5 3 Find the measure of each angle 4 5 Find m 1 1 6 x 8 2x

Y 2 Z 16 reflection across the x axis P y W y 18 reflection across the y axis Ay 10 X Boisinuos D doijet X X

20 rotation 900 origin D siter H 22 rotation 180 about the origin B Ay W T G y X H X 24 rotation 180 about the origin X orli 32010 OTSE

2 dilation of 2 5 6 4 reflection across the y axis R J F A H F R W y N X X

10 5 TT VE 10 0 5 is 5 X 10 A triangle on the coordinate plane has points located at A 1 6 B 4 3 and C 1 1 What is the area of the triangle I Submit of 9

20 A cross section of which of the following would show dark edges and brighter center when viewed in transmission mode with a MSP A B C D pr Round Carugo 10h 11 Flat Trilobal 8 en quant

14 140 Le 18 tan Find the exact value of each trigonometric function Create a right triangle lable all angles and find the sides of that triangle using sin cos tan cost 16 cos 17 cos 0 2 600 150 15 2 Fan 150 2 2 10 100 19 cos 450 870 450 360 40 cas

Line segment m has a length of 5 What is its length after each dilation Type the correct answer in each box Use numerals instead of words Round any decimal answers to the nearest hundredt For help see this worked example scale factor of 2 centered at the origin scale factor of 10 centered at the origin scale factor of 0 25 centered at the origin h

3 Student response use the graph to respond to each question Justify y 21 3x 1 y x 3x 1 X X a Identify the functions as a or b 5 10 J b From the graph determine the solution set explain c Solve the system of equations algebraically 10

The expression simplifies to an u 1 cos u 1 cos u X sin u cos u cos 2

28 45

The graph below shows the height of a burning candle over time Height of candle cm 10 Time Hours Question After how many hours will the height of the candle be zero otion road aloud After how many hours will the height of the candle be zero Explain how you figured out when the height of the candle will be zero Skip Question Scratch Paper Optional To Use Previous Question Functions 7 8 4 51 AC 9 6 x 1

A dilation with center P and scale factor 2 is applied to triangle ABC A 45 3 B Question What is the length of the image of segment AC under this dilation What is the length of the image of segment AC under this dilation Skip Question Scratch Paper Optional To Use I Functions 7 4 1 Previous Question 0 8 5 2 AC 9 6 3 11 X

Ava is 60 inches tall Jeremy is 25 taller than Ava This Question How tall is Jeremy How tall is Jeremy Skip Question Scratch Paper Optional To Use Functions 7 4 1 Previous Qu 0 8 5 2 AC 9 6 3

Figure ABCD is a square 2 B Question What is the area of ABCD here if you would like to hear this question read aloud What is the area of ABCD Skip Question Scratch Paper Optional To Use Functions 7 4 1 Previous Question 0 8 5 2 AC 9 6 3 11 X 1

A pizza restaurant sells a small square pizza 5 inch side length for 4 The pizza restaurant also sells a large square pizza with a 12 inch side length 5 inches 5 inches 12 inches 12 inches Question What should the cost of a large square pizza 12 inch side be so that both pizzas cost the same amount per square inch Click here if you would like to hear this question read aloud What should the cost of a large square pizza 12 inch side be so that both pizzas cost the same amount per square inch Skip Question Scratch Paper Optional To Use Functions 7 1 Previous Question 0 8 5 2 AC 9 x 6 3

Data was collected on housing prices in a local neighborhood Point A represents a mansion that a movie star lives in Frequency 0 1 x 125000 X XX XX XXX x X xx XXXX XX XXXXXXXXXXXXX XXXXXXX XXXXXXXX 250000 375000 500000 Home Price 625000 Click here if you would like to hear this question read aloud Point A 750000 X 875000 Question If point A is removed from the data set what would happen to the mean If point A is removed from the data set what happens to the mean of the data set Increase Skip Question Scratch Paper Optional To Use Decrease Functions 7 4 1 0 Previous Question 8 5 Stay the same 2 AC 9 6 3 X

The sun creates shadows for Julian and a nearby tree Julian is 5 feet tall and his shadow is 4 feet long At the same time a tree has a shadow that is 10 feet long A 4 ft 5 ft 10 ft Question What is the height of the tree Click here if you would like to hear this question read aloud What is the height of the tree Skip Question Scratch Paper Optional To Use Functions 7 4 1 Previous Question 0 8 5 2 AC 9 6 3 X

Question Write an equation that represents the graph of the linear function below Click here if you would like to hear this question read aloud Write an equation that represents the graph of the linear function below Skip Question Scratch Paper Optional To Use Functions 7 4 1 0 8 5 2 AC 9 6 3 X

Question What number goes in the blank to make this number sentence true 27 15 30 Click here if you would like to hear this question read aloud sentence true Skip Question Scratch Paper Optional To Use I Functions 7 4 1 Previous Question 0 8 01 5 2 AC 9 6 3 x T

Question Solve the equation below for x 1 6 7x 1 5 2 Skip Question Scratch Paper Optional To Use Functions 7 4 Previous 1 8 LO 5 2

Solve for the value of b 6b 7 7h 8

Solve for the value of n 37

Complete the square to find the vertex of the parabola y 5x2 4x 4 Enter your answer as a point h k including parentheses The vertex is at the point

The sonar of a navy cruiser detects a submarine that is r 3600 feet from the cruiser The angle between the water level and the submarine is 0 29 5 How deep is the submarine ft

The point is on the terminal side of an angle in standard position Determine the exact values of the six trigonometric functions of the angle 20 21 sin 0 cos 0 tan 0 csc 0 sec 0 cot 0 SE

What are the dimensions of the conference room in this floor plan Office Building Floor Plan Conference Room 12x12 12x5 12x12 12 36 12x8 12x12 12x12 12x12 48

28 29 30 Write a definition for a linear pair of angles Write a definition for a diameter of a circle Locate point C below so that A ABC is an isosceles right triangle AB dal B Swalen 101 8164 8 co Gy EN 4 6 6810

26 A prism with a hexagonal base 27 Circle R with an arc AB measuring 45

11 2 3 4 5 If the sum of the measures of two angles is 90 then the two angles are complementary A chord of a circle is a segment with both endpoints on the circle An acute angle is an angle whose measure is less than 90 The three basic building blocks undefined terms of geometry are planes points and lines A scalene triangle is a triangle with two sides the same length

6 7 8 9 10 A parallelogram is a quadrilateral with all the angles equal in measure If the measure of ZD is 77 then the reflex measure of ZD is 103 The ray from point L through point M is named as LM The length of line segment PQ is named as PQ The vertex of angle RST is point S to this

Sketch mark and label each figure 23 Rhombus RHOM with RO 1 HM 101 101 ontneg 24 Circle Q with diameter AB and tangent AT 25 An octagon OCTAGNUS with vertices S C A and N joined to form trapezoid SCAN su that SC I NA

16 Draw 3 different isosceles triangles below each with the same perimeter of 6x

Match each term at left with its figure at right 18 Right scalene triangle 19 20 Acute isosceles triangle 22 de Heptagon 21 Pyramid Prism ptomesng to tzaner for a b C d 250 e f h 140

Tell whether each statement is true or false 1 2 3 4 5 A polygon with ten sides is called a dodecagon If AB intersects CD at point P then ZAPC and LBPD form a linear pair of angles Point P is between points A and B and also between points C and D A rhombus is a quadrilateral that has exactly one pair of parallel sides If two lines do not intersect then they are not necessarily parallel A diagonal is a line segment in a polygon connecting any two vertices

In addition to the facts in the diagram which other statements are necessary to prove that AABC is congruent to AEFG by the ASA criterion O A W i and iii only OB i only OC iii or v only OD I or iv only 2 B 3 Reset LL 2 C i mzB mzF ii BC FG iii mzA mZE iv FG 3 v mzB mZE Next E G

Select the correct answer from each drop down menu A U The pair of triangles that are congruent by the ASA criterion is The pair of triangles that are congruent by the SAS criterion is F 5 S EN AD R 5 triangle BAC and triangle UTS triangle BAC and triangle RQP triangle PQR and triangle STU triangle BAC and triangle XYZ

Based on these segment lengths which group of segments can form a triangle OA 3 10 14 OB 8 7 13 OC OD 3 2 5 20 7 13

A building has a triangular rooftop terrace which is modeled by triangle ABC In triangle ABC the measure of ZA is 55 the measure of ZB is 65 and the measure of ZC is 60 Which side of the terrace has the greatest length O A BC OB AB OC AC O D Cannot be determined

Drag the image to the correct location Not all tiles will be used Triangle ABC is rotated 90 clockwise about point P to create triangle DEF Determine the correct orientation and location of triangle DEF AVA F W B E D F P

Which sentence best explains why shape 1 and shape 2 are not congruent 16 14 12 10 8 6 4 2 0 2 shape 1 4 6 T 8 shape 2 10 12 O A Not all corresponding pairs of sides on the two shapes are parallel OB There is no sequence of rigid transformations that will map shape 1 onto shape 2 OC Shape 1 cannot be mapped onto shape 2 using a reflection O D Shape 1 cannot be mapped onto shape 2 using a dilation OE Not all corresponding pairs of sides on the two shapes are perpendicular 14 16

9 5 x y46 7 y 5 9 3x y 0 M 10 8 6 4x 5y 5 8 3x 2y 210 10 4x y 3 30 zoom in 9 10 7 0 5 IS A SOLUTION TO THIS INEQUALITY True False 8 2 2 IS A SOLUTION TO THIS INEQUALITY True 1

If m28 23 find the measure of each missing angle Give your reasoning 4 F 5 6 3 a m 1 b m22 c m3 d m 4 e m 5 f m 6 9 m4