Geometry Questions

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

Use the figure for Questions 11 and 12 11 If ALMN is isosceles and T is the midpoint of LN which postulate or theorem can be used to prove AMLT AMNT A AAA B AAS C SSS 12 If AMLT AMNT what is used to prove 21 22 F CPCTC G definition of isosceles triangle N D SAS 11

Use the proof for Questions 9 and 10 Given L is the midpoint of JM JK NM Prove AJKL AMNL Proof Statements 1 L is the midpoint of JM 2 JL ML 3 JK MN 4 LJKL 5 LJLK 6 AJKLAMNL LMNL L MLN Reasons 1 Given 2 Definition of midpoint 3 Given 4 Alt int s are 5 Question 9 6 Question 10 9 What is the reason for ZJLK LMLN A definition of midpoint B corresponding angles C vertical angles D alternate interior angles 10 What is the reason for AJKL AMNL M 9

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

3x 13 12 and 2 Suppose cos 2x and tan 2x no decimals csc x x 2t Find the exact values of sin 2x and

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

2 Find the height of the tree www mathwarehouse com 30 43 h

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

he blade of a creu r saw rotales at a rate of 4000 revolubons per minute What is the inear velocity in miles per hour of a point on on the 5p of the outer edpe of a 7 t 4 inch diameter blade The linear velocily as approximately triles per hour Round to the at tanth ded 7

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

1 Find the closets point on the parabola y r 4 to the point 16 2

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

Right triangle ABC is shown A 3 m G 50 C a B Which equation can be used to solve for c sin 50 3 sin 50 O cos 50 O cos 50

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

Copy vectors u v and w head to tail as needed to sketch the indicated vectors a u v b u v w C U V d u w Choose the correct sketch for u v OA OB 4 Q O C Q W Q OD

6 If ACJW AAGS mLA 50 mLJ 45 and mLS 16x 5 what is the value of x F 17 5 G 11 875 H6 J5 45 A A 50 A4 16x 5

5 Which triangles are congruent in the figure FAABC AEBD G AABE ACBD HAAEB ACBD A B X LU

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

Given Prove A 4 BD AE BA CB 3 E DE CD B 1 2 D C

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

Calculator A rectangular lawn is 65 m long and 34 m wide Over time people have walked along a diagonal as a shortcut and have created a straight path What is the length of the path to the nearest tenth of a meter Enter your answer as a deicmal in the box 65 m 34 m

Calculator What is value of x Enter your answer in the box X 4 B 8 X 4 2x 1

Calculator BC is parallel to DE What is AC Enter your answer in the box units 10 D 8 B A C 15 E

Triangle ABC is similar totriangle DEF The length of AC is 12 cm The length of EF is 15 cm The length of DF is 9 cm What is the length of BC Enter your answer in the box 20 cm

continuing from 1 What is the distance between the two points shown in the picture 4 O 3 O 5 03 2 Ay 2 2 2 4 X

What equation will help you find the distance d between the two points pictured here 4 1 2 2 1 d O 2 1 d O 1 2 d 01 2 d 2 2 A 2 4 X

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

Provide the missing reasons for the proof Given CZE Prove AABC ADBE A B K D E

Flagpole a and flagpole c are both casting a shadow that ends at point s The distance x between the flagpoles is 12 m The distance y from flagpole c to point s is 10 m The height of flagpole a is 4 4 m What is the height of flagpole c

Expense Gas Insurance Oil Registration Depreciation Yearly cost or rate 500 00 400 00 100 00 100 00 20 What is the cost per mile over the course of a year for a 20 000 car that depreciates 20 with costs shown in the table and that has been driven for 10 000 miles A 0 26 per mile B 1 11 per mile C 4 11 per mile D 0 51 per mile

of transformation that ta 5 describe Sequence trapezoid ABCD to TSEU DOK MICK the sequence a

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