2D Geometry Questions and Answers

The area of the regular hexagon is 169 74 ft2 7 ft What is the perimeter rounded to the nearest tenth O 24 2 ft 28 3 ft O 48 5 ft O 56 8 ft

Bianca calculated the height of the equilateral triangle with side lengths of 10 tan 30 h 8 7 h A 30 Then she used the formula for area of a triangle to approximate its area as shown below bh 10 8 7 43 5 units2 5 Calculate the area of the equilateral triangle using the formula for area of a regular polygon and compare it to Bianca s answer The apothem rounded to the nearest tenth is units The perimeter of the equilateral triangle is Therefore the area of the equilateral triangle is or approximately 43 5 units V The calculated areas are units

Manuel wants to buy a window shade to cover the window and frame shown The window is in the shape of a regular octagon The radius of the window including the frame is 2 ft and the measure of each edge of the octagonal frame is 1 52 ft Window 1 52 ft What is the approximate area of the window that nee to be covered including the frame O2 ft O 7 ft O 11 2 ft O22 5 ft

A community pool that is shaped like a regular pentagon needs a new cover for the winter months The radius of the pool is 20 10 ft The pool is 23 62 ft on each side To the nearest square foot what is the area of the pool that needs to be covered O192 ft O 960 ft O 1 921 ft 3 842

A regular pentagon has an apothem measuring 3 cm and a perimeter of 21 8 cm 3 cm What is the area of the pentagon rounded to the nearest tenth O 13 8 cm O 17 3 cm O 32 7 cm O 69 0 cm

A hexagon has a radius measuring 23 cm What is the approximate area of the hexagon O 686 6 square cm O 793 5 square cm O 1374 4 square cm O 1587 0 square cm

A regular pentagon has a perimeter of 60 cm B A D What is the measure of angle CBD What is the length of segment CD cm Which trigonometric ratio can be used to compare Bo to CD using angle CBD What is the approximate length of BC cm What is the approximate length of BD GM

Probability and Counting 6 A fair die is rolled once Let A be the event of rolling a number less than 4 Let B be the event of rolling an even number A 4 1 Draw a Venn diagram 2 What is the probability of event A P A 3 What is the probability of event B P B 4 What is the probability of A and B P AnB 5 What is the probability of A or B P AUB

The floor of a gazebo is in the shape of a regular octagon The perimeter of the floor is 72 feet The distance from the center of the octagon to one of the vertices is 11 8 feet What is the approximate length of the apothem 3 feet What is the approximate area of the floor of the gazebo square feet 3

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