2D Geometry Questions and Answers

13 Find the value of x A 5 B7 C 10 D 15 M x 3 TA 5 W

Here is a rectangle with some triangles inside it B E C A F D A Which triangles are similar to triangle AED Explain or show your reasoning B The length of segment EF is 16 units and the length of segment ED is 20 units Find th length of segment FA Explain or show your reasoning X 2 m 53 B 22 BIUS X x

13 Find the value of x A 5 B7 C 10 D 15 x 3 TA 5 W M

A cylindrical cup measures 12cm in height When filled to the very top it holds 780 cubic centimeters of water What is the radius of the cup rounded to the nearest tenth Explain or show your reasoning

Consider this figure F graphed as shown A Transform figure F using the rule x y x 1 y 2 Size Undo Clear All O F 5 5 0 5 10 5 B Describe the transformation precisely C Does the transformation result in a figure that is congruent to the original similar to th original both or neither

12 Find the possible values for mz 1 F 180 mz1 62 G 90 m 1 62 H0 mz1 62 Jmz1 118 62

11 Which of the following could be a possible equation for a circle with a diameter of 30 a x 1 y 30 b x 8 y 8 225 c x 2 y 3 15 x y 900 d 12 Deter whole a b C d

11 Which assumption Ax 5 would you make to indirectly prove x 5 Cx 5 Bx 5 Dx 5

10 Which of the following points does NOT lie on the exterior of the circle given by x y 6 16 a 6 0 b 4 1 c 2 2 d 0 2

7 Circle M has a diameter with endpoints 5 9 and 7 7 Determine the length of the radil a 20 b 40 C 10 d 5 Habib to cuticus 90

9 Determine the diameter of a circle with an area 628 mm a 28 mm b 24 mm C 30 mm

12 The circumference of circle Z is 124 inches Determine the diameter of the circle to the nearest whole number a 124 b 39 C 20 d 19

Write the letter for the correct answer in the blank at the right of each question For Questions 1 4 refer to the figure at the right 1 Name an altitude A DE BAB 2 Name a perpendicular bisector F DE GAB 3 Name an angle bisector A DE BAB 4 Name a median F DE GAB C GB D CF HGB C GB HGB B D J CF D CF J CF

13 The center of a circle is 1 2 and one point on the circle s circumference is 3 5 What is the length he diameter

Area 4 Determine the equation of the circle Center Radius quation 4 3 2 5 4 3 2 1 1 2 3 4 5 1 2 3 4

d 393 ft 3 A circle is centered at C 1 3 and has a radius of 6 Where does the point P 6 6 lie a Inside the circle b Outside the circle C On the circle

5 Which of the following is with center at 1 12 and a diameter of 10 a x 1 y 12 100 b x 1 y 12 10 c x 1 y 12 5 d x 1 y 12 25

1 Identify the center and radius of the equation below x 7 y 2 96 a 7 2 r 48 b 7 2 r 4 6 7 2 r 48

2 Write an equation for a circle with a ce 11 14 and an area of 16

1 James family wants to enclose their circular garden with a fence Given that their garden is 125 ft wide to the nearest foot what is the minimum length of fencing they need to buy a b 56 ft 246 ft 366 ft 7 X

2 Which equation represents a circle with a diameter of 18 and a center of 4 8 b a x 4 y 8 18 x 4 y 8 81 x 4 y 8 9 c 1 x 8 324

For Questions 5 7 refer to the figure to determine which is a true statement for the given information 5 AC is a median A m2 ACD 90 BLBAC LDAC 6 AC is an angle bisector F mL ACD 90 7 AC is an altitude A mL ACD 90 GLBAC LDAC B LBAC LDAC C BC CD DZB LD HBC CD C BC CD B JLB LD DZB LD

8 Name the longest side of ADEF F DE GEF HDF J cannot tell D E 62

13 What are the missing coordinates of this triangle A 2a 2c C 0 2a B 2a 0 D a 2c a c L 0 0 N Bonus Classify the triangle with vertices at A 5 0 B 0 5 and C 5 0 13 B

7 Are the pair of triangles is congruent If yes include the theorem or postulate that applies A yes LA B yes HL C yes HA D no 7

8 A triangular shaped roof of a house has congruent legs What is the measure of each of the two base angles F 25 G 50 H 100 J 120 80 8

6 If ACJW and m2S F 17 5 G 11 875 AAGS mLA 50 mLJ 45 16x 5 what is the value of x H6 J5 C 45 W A 50 16x 5 S 6

C CD Find the value of x A B 2x 3 5x 12 D

The measure of minor arc AE 120 and the measure of minor arc BD 58 What is the m BCD 120 A E B 58 D

A sector of a circle of radius 1 5m has an area of 25m Find the central angle of the sector Do not round any intermediate computations Round your answer to the nearest tenth radians X S

The area of a sector of a circle with a central angle of 150 is 18m Find the radius of the circle Do not round any intermediate computations Round your answer to the nearest tenth m

D This table shows the top scoring teams in the National Hockey League for the 2017 2018 regular season NHL com Team Tampa Bay Lightning Winnipeg Jets Pittsburgh Penguins Toronto Maple Leafs Vegas Golden Knights Total Goals 290 273 270 270 268 Points 113 114 100 105 109 112 80 267 Boston Bruins New York Islanders Nashville Predators 261 261 Washington Capitals 256 Colorado Avalanche 255 a Without the use of technology create a scatter plot of the data 105 95 marks

5 Find all of the unknowns in this figure using special right triangles 24 45 a X 20 b d 130 C

3 Find the missing sides in the triangle 30 B

4 Suzie sees a plane at 10 000 feet above sea level headed straight for her boat at a 30 degree angle of depression What is the horizontal distance between her and the plane And how much further does the plane have to travel before it hits her boat EXAMPLE PROBLEM 1 10 000 60 90 W 30 X 30 z

1 What is the measure of the other 2 sides in this triangle 45 P 80 m T

Consider the quadratic function f x x 2x 3 Determine the following enter all numerical answers as integers fractions or decimals The left most x intercept is The right most x intercept is a The y intercept is y The vertex is The line of symmetry has the equation

2 What is the measure of ZB A 52 B 14x 6 y C

1 Draw in the appropriate amount of isosceles triangles to fill the regular octagon 6 feet 2 Use the isosceles triangles to find the perimeter of the octagon 3 Calculate the area of the octagon

1 A baker creates fantastic cupcakes that can each be comfortably enclosed in a cube of side length 2 in and a square base She wants to deliver these cupcakes to stores in batches of 75 in a large box that has 3 layers of cupcakes What is the volume of the box and what is its surface area 2 A tennis ball container has a 2 inch diameter and holds 3 tennis balls Find the volume of the container the volume of the tennis balls and the volume of air in the can 3 A pyramid has a square base 60 by 60 The slant height is 50 Find the volume of the pyramid as well as how much glass would be needed to cover the faces

5 Are the 2 triangles right acute or obtuse 1 60 3 2 30 1 450 1 45

What is the length of BC Round to the nearest tenth B X C 6 8 cm 7 5 cm 16 cm 65 A

TIM A triangle has angles that measure 30 60 and 90 The hypotenuse of the triangle measures 10 inches Which is the best estimate for the perimeter of the triangle Round to the nearest tenth O 20 0 in 23 1 in 23 7 in 27 4 in

Which equation can be used to solve for b B 30 8 ft 4 Ob 8 tan 30 8 tan 30 O b 8 sin 30 8 Ob b G C 6 A

Given A ABC FC BA and AF bisects ZBAC Prove AB AC BD CD B A D F C Note Image not drawn to scale

In A FEG point His between points E and F point J is between points F and G and HJ EG CH 14 HF 26 and FG 60 What is FJ ter your answer in the box J 39

The diagram below shows the cross section of a cylinder of radius 2 5 m A belt is wrapped around the cylinder and passes through a point 5 metres from the centre of the cylinder 5m

WE DO 3 In circle C above m B 11x 10 and m ADB 3x 15 Find the value of x and mZACB A D C B

3 In circle C above m B 11x 10 and m ADB 3x 15 Find the value of x and m ACB A FEXAMOS D C B

7 Find the length of TV T U 14 7 4 6 X 1