Geometry Questions

1 Roof trusses often use right triangles to make a flimsy 2 x 4 more rigid to hold up the weight of the roof A house is 40 feet wide and the roof is an isosceles triangle with base angles of 30 How far is it from the bottom edge of the roof to the peak Round your answer to the nearest tenth

30 4034 x 6 60 2 3

Example with CB length of CD and DB 1 Given triangle ABC 5 Determine the A 30 503 5 D 60 5 B

Convert a speed of 105 mi h to units of feet per minute Also show the unit analysis by dragging components into the nit factor slots 105 mi 1h 60 s 1 ft X 60 h Answer Bank 1h 3 ft 1 min 12 in 60 min 1 mi 5280 ft II ft min

21 11 9 yd LA C 9 5 yd AB A 7b 9 5 11

Find the value of the variable c if Y is between X and Z on a line segment XY 2c 1 YZ 6c XZ 81

2 Solve the triangle by finding all missing sides and angles Round all values to the nearest hundredth 6 T 117 N

Explain what is meant by the statement cos 0 9 25 84

In AABC m A 90 and cos B 0 392 Find the measure of angle C

ADEF and AHJK are both right triangles If cos F cosK which of the following statements is true A m F m K B sin F sin K C ADEF and AHJK are similar D All of the above

4 If ZILF find tan G J 12 D

1 Find m W Round to the nearest hundredth 18

7 In right triangle MJK the hypotenuse is 1 75 times longer than the side opposite accute angle K Find the measure of angle K to the nearest hundredth

5 Which is greater m M or m R Give a reason for your answer P 0 6 0 4

0 The percentage grade of a road measures the change in the altitude of a road in comparison with the horizontal distance covered by the road For example a 5 grade means that the road rises 5 feet for every 100 feet of horizontal distance Ms Palmer is about to turn onto a mountain road and sees this sign What angle does the road make with the ground 9 8

2 Find m H and mZJ Round to the nearest hundredth 13 H 12

6 5 4 6 All solutions require proper format as modelled in class Communication marks as assigned where indicated in the question to evaluate the clarity of the solution Up to TWO communication marks for proper mathematical formatting Knowledge and Understanding 1 Determine the coordinates of the midpoint of each line segment a J 0 2 1 5 and K 3 6 0 2 1 5 3 5 2 marks

7 Quadrilateral MATH has vertices M 6 4 A 4 2 T 0 1 H 1 8 What are the vertices of the image after a dilation with a scale factor of using the origin as the center of dilation

In 6 Given the preimage and image state the coordinates of each figure and the scale factor of the dilation with center at origin Answer in simplest fraction form 6 10 6 8 4 2 O A D 2 A D 4 B C 6 8 10 A A Scale Factor B B C D D

Solve each proportion round answers to the nearest tenth 5 3 6 1 12 7 2 8 x 3 3 x 8 6 x 1 4

In 4 5 describe the dilation and state the scale factor Solid is preimage 4 5 12 cm 3 cm 8 in 6 in 20 in 15 in

Water flowing through both a small pipe and a large pipe can fill a water tank in 9 hours Water flowing through the large pipe alone can fill the tank in 17 hours Write an equation that can be used to find the amount of time t in hours it would take to fill the tank using only the small pipe Round to the neares whole hour

9 True or False Give a reason for your answer 4 then the side adjacent to must be 4 and the hypotenuse must be 5 5 a If cos 0 b If tan 0 1 5 then the side adjacent to is 13 the length of the side opposite 0

7 In ARST sin R 0 8 Find two possible sets of side lengths for ARST S R S T T

4 Find RP and KR to 2 decimal places 55 K 4

3 Find PR RM Round to 4 decimal places P 54

8 ARST is shown not to scale Is RS greater than less than or equal to ST Explain how you know 9 True or False Give a reason for your answer R S 35 T

3 Two diameters of a circle of radius 15 inches are drawn to make a central angle 48 A smaller circle is placed inside the bigger circle so that it is tangent to the bigger circle and to both diameters What is the radius of the smaller circle 48

We need a second quadrant angle se From the figure 0 ses x for which cos sin e cos e 2 Thus csc 0 2 for the following values 0 Use 0 2x Enter your answers as a comma separated list e

Step 1 of 4 The relationship between csc 0 and sin 0 is csc 0 Step 2 of 4 Since sin 0 Step 3 of 4 1 csc 0 0 1 The figure above shows that in the first quadrant sin 0 sin and we are given csc 0 2 it follows that sin 0 Submit Skip you cannot come back 1 2 when 0 The only other quadrant where sin 0 is positive is the Select adrant second third fourth sin 0 1 and thu

Since sin 0 1 CSC 0 and we are given csc 0 2 it follows that sin 0 2

9 Translate the grasshopper right 4 and up 3 Ty pre image 2 2 4 2 0 20 4 X

If we rotate Triangle ABC 180 about the origin where would B be located 6 A B 5 5 1 5 1 1 5 1 5 O 2 2 2 3 4 5 6

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E A JKL has vertices J 6 2 K 1 3 and L 7 0 What are the vertices of the image after a dilation with a scale factor of 12 using the origin as the center of dilation

ADEF has vertices D 8 4 E 2 6 and F 3 1 What are the vertices of the image after a dilation with a scale factor of 5 using the origin as the center of dilation

AABC has vertices A 8 4 B 14 16 and C 6 10 What are the vertices of the image after a dilation with 1 a scale factor of using the origin as the center of dilation 2

7 AGHI has vertices G 0 20 H 16 24 and I 12 12 What are the vertices of the image after a dilation with 3 a scale factor of using the origin as the center of dilation 4

9 Graph Quadrilateral MNPQ M 1 3 N 3 3 P 2 3 Q 1 3 then state the coordinates and graph the image after a dilation with a scale factor of 3 using the origin as the center M N P Q

8 7 5A R 4 3 2 1 O R PO 1 2 3 4 S is T 5 6 7 S T 8 9 T X 10 Q Q

Sila In 1 2 State type of dilation and scale factor answer in simplest fraction for 2 12 in 12cm A 8 cm C 4 cm 8 cm B A A D D 9 in 6 in B C B 8 in

A A 3 0 2 4 12 10 B 6 20 18 A B 2 Ja Factor 6 B B G B 10 12 14 C 16 C 18 20

Review The graph of the linear function g x is shown belo AY What is the slope of the line 0 2 4 3 5 04 2 g x 3 2 1 31 1 2 3 41 5

Review What is the equation of the following parabola in vertex form 54 3 2 1 N 11 4 21 31 45 st A Oy x 1 3 Oy x 1 3 y 8 x 3 1 y 8 x 3 1

3 In the following drawing each segment is tangent to each circle The largest circle has a radius of 3 cm the medium circle has a radius of 2 cm What is the radius of the smallest circle

2 y x 2 5 4 3 2 1 4 4 y x 4 54 3 2 1 6 y 4 3 2 1 7 2 Ay 2 A X XY

A Stop 1 81 hard

form of the equation of the line through the given points 2 through 1 5 and 5 1 Write the slope intercep 1 through 2 5 and 0 1 Y 2x 1 3 through 0 5 and 1 2 X 3x 5 5 through 2 2 and 1 3 x 1x 4 7 through 1 4 and 0 1 3x 1 9 through 0 2 and 4 2 1x 2 1xt 4 4 through 3 2 and 5 4 Interce 6 through 0 1 and 1 3 4 8 through 4 4 and 5 2 x x 10 through 2 5 and 0 1 Y 3x1

Find the slope of each line 1

Find 1 ope intercept Form Worksheet the slope of each line 3 Siope O 2014m 2 9 15 9 14 9 4 Name 3 lopp 0 Find the slope of the line through each pair of points 7 14 20 5 9 6 Date stope 1 SI 8 1 1 5 6 10 2 12 18 15 Period