2D Geometry Questions and Answers

The radius of a regular decagon a 10 sided figure is 15 units The length of one side of the polygon measures about 9 3 units What is the approximate area of the regular decagon rounded to the nearest tenth O273 6 square units 0547 3 square units 663 1 square units 1069 9 square units

The area of the octagon below is 10 391 9 square millimeters 56 mm What is the approximate perimeter of the octagon Round to the nearest whole number mm What is the approximate length of one side of the octagon Round to the nearest whole number mm

The sum of all but one interior angle of a heptagon is 776 What is the measure of the final interior angle O 42 O 56 O 124 304

What is the sum of the measures of the interior angles of a 12 gon O 1620 O 1800 O 1980 O 2160

77 66 59 62 12x What is the value of x O 6 O 8 O 10 O 12

6 5 4 3 2 6 5 4 3 2 1 2 3 4 6 The graph above is a transformation of the function x Write an equation for the function graphed above

10 5 4 3 2 6 5 4 3 2 1 2 3 5 1 2 3 4 5 2 The graph above is a transformation of the function Write an equation for the function graphed above

Write an equation for a line that passes through the origin and is perpendicular to y 5x 2

Enter the letter for the function graphed below a y x 2 b y x 2 c y x 2 2 d y x 2 2 e y x 2 Enter

Which sequence of rigid motions will definitely work to take triangle STU onto triangle GHJ S 111 H Rotate STU clockwise 90 degrees around point T Translate S T U to the left 1 unit Translate STU to the right 8 units Reflect S T U over HJ Reflect STU over ST Rotate ST U clockwise 180 degrees around point I 1p

Enter the letter for the function graphed below 3 a y x 2 b y x 2 c y 3 3 x 2 2 x 2 2 d y e y x 2 Enter

Prove that ABCD is not a parallelogram 9876543N 2 1 A O B D 1 2 3 4 4 5 5 6 6 C 7 7 8 9 X

What is the volume of the following figure Please explain how you got your answer 3 in 8 in 11 in

14 In the circle MN is a tangent and MK is a secant If ML x 3 LK find NM x 3 x 3 x 48 16 and MN x 3 K x 3 M L 16 x 3 N

Solve for x Round to the nearest tenth if necessary F 8 8 X 72 E

15 In the accompanying diagram LN and LS are secants If LM 4 NM KS x 5 find the length of LN S x 5 8 LK 3 and N x 8 M K 3 4

A B 10 7 D U 8 19 LL 13 F Lin knows that angle A is congruent to angle D She claims that triangles ABC and DEF must be similar Convince Lin that the triangles are not similar

the width w of the rectangle cm Your width measurement

Three vertices of Parallelogram PQRS are shown Q 8 5 R 5 1 S 2 5 Fill in the statements and reasons in the table to complete the proof to show that Parallelogram PQRS is a Rhombus 1 2 SR QR SR QR PS QR 6 Parallelogram PQRS is a shombus Statement 1 Select Statements Statement 2 Select Reason 2 Select Statement 6 Select Reason 6 Select D Pythagorean Theorem 2 Substitution Definition of congruent line segments Property of a parallelogram 6 Definition of a thombus Reasons

Cool Down Finding Unknown Values in Right Triangles Find the lengths of segments AB and BD Then check your answers using a different method 3 2 I D 3 1 8 C

similar U SSS SAS AA W F G none of the above the triangles cannot be proven similar Write a similarity statement E

2 AB and AD are tangent to circle Q Find the value of B X 8 5x 4 Q D

Find the following in circle P K 84 P 73 N L M 3 arc MN x 3 4 4 are LM 5 ZJPN

15 Find the volume of the pyramid 20 m 30 m 24 m

Find the exact circumferenc 5 area 196 mi

Find the length of the hypotenuse Round your answer to the nearest hundredth 7 Show Your Work 4 O 9 95 8 06 3 32 O 11 00

Use these two triangles to answer questions 7 and 8 Given ZA 50 ZB 100 AABC APRO B A 14 What is mzQ OA 20 OB B 30 OC 50 O D D 100 22 4 C P 20 R 32

Required GivenDE BC Which proportion is justified by the image A 18 18 24 28 34 24 32 8 O 18 24 O 18 24 24 8 8 O 18 2 4 24 D 6 C E 8 B

Required Given AKLM ARST Which congruent statments would be true K M Show Your Work R OKMRT and LK ST OKMRT and LM LS OLKLR and KM RT OZKLR and ZM ZS

Based on the diagram which congruence statement is true B AC DE ZACB LEDC ZC ZD

AQRS has a perimeter of 55 If RT bisects LR What is the length of segment QT R Q 10 12 18 T 12 S

Required Which statement is true Ay M 8 6 4 2 8 a 2 2 4 6 8 Triangle LMN is an equilateral triangle Triangle LMN is a right scalene triangle Triangle LMN is a right isosceles triangle Triangle LMN is an acute isosceles triangle

15 Which of the following graph is Hamiltonian H A G1 B G1 G2 C G3 G4 D G4 G P m G4 4 1

Relative to angle G which side is the adjacent side E M Choose 1 answer A GE G

Given the following unit circle rotate green dot to the appropriate angle and then find the exact value of the function sin 45 y

Find the height of the pyramid 10 1 mi 9 mi 9 mi

Solve for x 8 x Simplify your answer Type an integer or a simplified fraction

Question 11 Square ABCD is transformed to create image A B C D as shown 4 D C 2 4 2 y 0 A P 2 B B A 2 C D 4 X Select all of the transformations that could have been performed O a rotation of 180 degrees clockwise about the origin a reflection across the line y x O a reflection across the line y 2x O a rotation of 270 degrees counterclockwise about the origin and then reflection acros x axis

Circle is shown with points A B C and D on Circle O A D 20 0 C mZAOB B If z 50 what is the value of y and the angle measurement of ZAOB Drag a tile into each box degrees 4

Quadrilateral BCDE is shown on the coordinate grid Keisha reflects the figure across the line y x to create B C D E What are the coordinates of E 10 10 8 6 4 2 Y 8 6 4 2 01 2 41 6 8 10 2 B 4 6 10 8 10

Question 8 The proof shows that opposite angles of a parallelogram are congruent Statements ABCD is a parallelogram with diagonal AC ABCD and AD BC 22 23 21 24 m 2 m3 and mz1 m 4 m 1 m 2 m 4 m 2 mel m 2 m 4 m 3 m l m 2 m BAD m23 mz4 m DCB m BAD m2DCB BAD DCB What is the missing part of the proof O Angle Addition Postulate O Substitution O Alternate Interior Angles are congruent Reasons Given Definition of parallelogram Altemate interior angles are congruent Measures of congruent angles are equal Addition property of equality Angle addition postulate Substitution Angles are congruent when their measures are equal

Find the volume of the rectangular prism 3 m 11 m 3 m

6 Prove if QR a tangent of the circle S Use the Pythagorean theorem a b c R O 14 S 19 25

4 Find the value of x 9x 1 C E 41 5x D F

18 Find missing lengths of the 45 45 90 triangle Y Remember to give answers in simplest radical form X 5 y x x

23 Find missing lengths of the 45 45 90 triangle Your answer should be in simple radical form The triangle is a 45 45 90 triangle 25 X y y x x X

8 Find the measure of arc QU U 46 R T35 S

20 Find the missing angle measure using sine cosine or Remember to use SOH CAH TOA to help you 10 O X O x 34 O x 42 x 56 x 48 15

22 Sum of Interior angles in a polygon Find the value of x using the sum of the interior angles of the polygon 6x x 28 x 20 0 x 8 x 19 120 8x 8 1x 5x 6 4x 14

5 Properties of parallelograms Find the value of x and the measure of the smaller angle for the consecutive angles of the parallelogram x 114 6x The measure of the smaller angle is degrees