2D Geometry Questions and Answers

A floor plan for a new modern home is modeled by a regular nonagon and a regular triangle as shown below K What is the measure of JKL Type your answer

Given AABC ALMN B 5 11 12 What is the length of AC 22 x 5 24 x 4 M 10 3x 1 3x 3 N

A floor tile is designed with a regular pentago on the center of the tile with its sides extended What is the value of x to

Directions Type your answer in the box below If ABCD is a parallelogram what are the coordinates of B y A 2 3 D 0 0 B C 5 0 x

A 20 foot ladder is leaning against a building and makes an angle of 60 with the ground How far is the base of the building to the foot of the ladder 5 ft 8 2 ft 10 ft 17 3 ft 20 ft 60

The figure has angle measures as shown A 3x What is the measure of BCD Type your answer 5x 10 D 3x B

b 7 8 5 6 21 and 26 23 and 28 42 and 47 Which pair of angle pairs are NOT supplementary Co 1 2 3 4

On the shores of a river surveyors marked locations A B and C The measure of ZACB 70 and the measure of LABC 65 List the distances between these locations from shortest to longest down below Shortest 1 2 3 A to C A to B B to C A B AM C

Given AC BD AD BC Which postulate could be used to proveADCA ACDB D ASS AAS SAS SSS A E B C

Triangle ABC and EFG are similar with the measurements shown G C AA 7 A 5 B E 10 F What is the measure of GE

The container is composed of a right circular cylinder and a right circular cone 13 ft 1 243 ft 490 ft 754 ft 10 ft 24 ft What is closest to the surface area of the container 1 696 ft

Two cylinders a sphere and a cone are shown Select the two objects with the same volume 4 cm Figure A 3 cm Figure A Figure B Figure C Figure D Figure B O 4 cm Figure C 2 cm 4 cm T 2 cm Figure D 6 cm

A fish tank in the shape of a rectangular prism has these dimensions length 20 inches width 10 inches height 12 inches What is the volume of water in the tank when it is full 3 000 cu in 2 400 cu in 1 120 cu in 1 920 cu in

Which is closest to the total surface area of a cylinder with a radius of 5 inches and a height that is equal to its diamter 596 sq in 785 sq in 314 sq in 471 sq in

A rectangular prism is shown 18 in 12 in 24 in What is the surface area of this prism 936 sq in 5 184 sq in 1 872 sq in 156 sq in

If a cube with a side length of 6 inches had it s dimensions cut in half what would be the volume of the new cube 108 cubic inches 54 cubic inches 27 cubic inches 9 cubic inches

A rectangular prism is shown 8 cm 9 cm 12 cm What is the volume of the pyramid 108cm 864cm 288cm 432cm

A pizza has a diameter of 16 inches Which is closest to the area of one slice if the pizza is divided into 6 equal pieces 134 1 sq in 67 2 sq in 117 1 sq in 33 5 sq in

Sarah is filling a glass sphere with decorative sand The radius of the sphere is 2 inches Which is closest to the minimum amount of sand needed to completely fill the glass sphere 100 5 cu in 10 7 cu in 25 1 cu in 33 5 quin

A concrete pillar shaped as a rectangular prism is designed as follows 9 5 m 1 5 m 1 5 m 14 3m 28 5m 21 4m

A sphere has a diameter of 10 inches What is the surface area of the sphere 415 69 207 85 277 13

A cylinder has a diameter of 10 inches and a height four times its radius What is its volume 2 000 cu in 4 000 cu in 40 000 cu in Foo

Find the minor angle in degrees of the triangle with measures 4 6 and 7

Question 9 The image below is a cartoon of a planet with an elliptical orbit around a star Th e star is the focus of the ellipse There are na mes for the points in an orbit where a planet is closest 1 and furthest from the star 2 Co nsult your notes or text and enter the correct n ames in the spaces below Answer 1 Page 4 Star a 2 Planet The furthest point that a planet reaches from the star it orbits in the image is called

semimajor axis Study the image below each square is 1 cm Use the squares to measure distances Answer Then using the above formula calculate the eccentricty value for the elipse below Enter your answer in the pace provided UT a 1 cm Question 8 The image below is a cartoon of a planet with an elliptical orbit around a star Th e star is the focus of the ellipse There are na mes for the points in an orbit where a planet is closest 1 and furthest from the star 2 Co nsult your notes or text and enter the correct n ames in the spaces below Page 3 1 Answer Star a Planet

7 Find m2B mzC and mzD A 104 71 B

2 In the diagram television cameras are positioned at A and B to record the news anchors at the desk The desk is an arc of A You want to move Camera B so that m B is 30 Should you move the camera closer or farther away How does this affect mCD Explain your reasoning 80

3 What is the value of x H X 20 I 4 What

Assume we have 120 pieces of rectangular tiles of dimensions 15 x 20 cms How many pieces of such tiles could be used to create a square All tiles should be placed in the same direction Select one O a None of the remaining possibilities is correct O b There are more than 5 soulutions to this problem O C No square can be constructed The sum of all solutions is 168 O e The product of all solutions is 480 Od

3 21 Determine the moment about point A for the forces shown in Figure P3 21 3 m 5 KN B 75 2 m A FIGURE P3 21 2 kN 0 Q 2 kN 5 m

5 Find the measure of each arc of OC where AB is a diameter a AB b DBA c BDA

Find the angle of the sector given the radius and the area of the sector Radius 12 ft Area of sector is 339 3 ft 90 degrees 210 degrees 270 degrees 118 degrees

Find the area of the sector O 398 2 ft O 381 7ft O 158 4 ft O 159 0 ft 13 ft 270 Nong of the other answers are correct

How many degrees is radians 12 O 30 degrees O 100 degrees O 120 degrees O 105 degrees

Determine the equation of the circle graphe below 10 9 8 7 6 5 4 3 2 1 10 9 8 7 6 LO 4 3 2 1 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9

below 10 9 8 7 the equati 6 5 4 3 2 1 y 10 9 8 7 6 LO 5 4 3 2 1 1 2 3 4 5 6 7 8 9 of the 1 2 3 4 5 6 graphed 7 8 9 10

Given the arc length find the radius of this figure A O 17 5 O 34 6 O 3 5 O 14 9 72 rcm 22 cm B

Find the missing angle and arc measures for the following figure E D LEAF DC DBF LEAD A 60 52 C LL F B

Date Perios In each triangle M N and P are the midpoints of the sides Name a segment parallel to the one given 1 C 2 CD 5 Find the missing length indicated 3 Find CD 16 5 Find XJ 7 Find DF g D 13 IQS 4 Find AC 6 Find IK 18 8 Find PQ 0

any final answer ALL WORK must be shown in order to 1 In the circle above point A is the center and the length of arc BC is of the circumference of the circle What is the value of x B A 24 to

Theorem Theorem 6 11 Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side AB BC AC Proof Ex 47 p 342 AC BC AB A AB AC BC Ex 1 Tell whether a triangle can have sides with the given lengths Explain 3 5 7 Ex 2 Tell whether a triangle can have sides with the given lengths Explain 4 6 5 11 8 5 13 B Ex 3 The lengths of two sides of a triangle are 6 centimeters and 11 centimeters Find the range of possible lengths for the third side x 4 The lengths of two sides of a triangle are 22 inches and 17 inches Find the range of possible ngths for the third side

Ex 1 Given AB DC ZABC ZDCB Prove ZA ZD Ex 2 Given M is the midpoint of PQ and RS Prove QR PS R CO B A D

Find the cosine function of the graph below A y 3 2 1 0 2 3 1 2 3 5 0 7 8 10 x

What is the area of the figure Round to the nearest tenth 9 ft 13 ft 5 ft

Directions Circle or write the correct response to each problem below Type of Slice The Slice is Parallel Horizontal Name the Cross Section 1 Perpendicular Vertical Angled

13 12 11 10 8 7 6 5 4 3 2 1 1 f x 2 sin TU X K 2 5 3 The curve above is the graph of a sinusoidal function It goes through the points 7 2 and 3 2 Find a sinusoidal function that matches the given graph If needed you can enter 3 1416 as pi in your answer otherwise use at least 3 decimal digits 2 3 4 6 a X

2 Determine the value of the angle Y 110 A 52 C 29 Z B 73 D 31 146

the circle C below mzBCA x 12 and mAB 3x 24 What is the mzAFB7 a 15 b 30 c 48 d 60 b If the measure of major arc DFA 240 determine m ACD

1 In the diagram above of circle 0 mzAOC 3x 5 and m ABC x 15 What is 5 b 20 25 d 40 80 a C e A B C

In circle O below AB is a diameter Use the given measures to determine all other missing C m AOC mCB mLAOD mBD MAD 120 A X 89 D B