Geometry Questions

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

y 3x 3 5 1 1 2 10 25 y 2x 4 27 y y x 1 2 435 410 6 3 4 2 10 2 2 2 24 y 2x 2 342 10 26 y x 3 di a 5 28 y x 5 34 35 10

29 y x 5 434 3 31 y x 2 33 y 3x 1 0 5432 0 40 2 3 3 x 1 30 y 2 2 In 44 33 10 4 32 y x 1 44 3 6 10 34 y x 1 d 0

1 Find a situation that can be modeled using similar triangles 2 Take a picture or sketch the situation 3 Use the scale factor to determine the lengths of all sides of the triangl

ry 23 Hanna Anguiano CA Geometry B Illuminate Credit 1 pdf 1 Which of the following properties is true about 2 Which of the following properties is true about ALL parallelograms Choose one ALL parallelograms Choose one A B C Four right angles Diagonals are bisected Only one pair of parallel sides 3 If x 9 can it prove ABCD is a parallelogram Show your work below B C 105 11x 6 D 5 Solve for x using the property of bisected diagonals CN 20 LN 6x 2 OA B C Opposite sides are equal and parallel All angles are always equal The sum of all angles is 180 4 If x 7 can it prove BCDE is a parallelogram Show your work below E 115 9x 7 100 D I 6 Solve for x using the property of bisected diagonals Then find the measure of VX VH 18 U HX 4x 6

T 18x 7 V 65 7x 5 U x 2 Hri 2x 2 R I 3 Solve for x in the parallelogram below Then find 4 Solve for x in the parallelogram below Then find the measure of ZY the measure of ZT U l 6x 6

etry 23 Hanna Anguiano CA Geometry B Illuminate Credit 1 pdf 5 ABCD is a parallelogram Determine whether each statement must be true Select the correct answer for each lettered part A The perimeter of ABCD is 2AB 2BC B DE DB C BC DC D ZDAC ZBCA E AAED ACEB F ZDAC ZBAC O Yes O No O Yes O No O Yes O No O Yes O No O Yes O No O Yes O No A 100 I Optional Complete problems 6 7 10 13 17 18 24 from your textbook on separate lined paper for extra practice When you are finished check the odd problems for solutions at the back of the textbook 11

1 Does each set of given information guarantee that quadrilateral JKLM is a parallelogram Select yes or no for each situation A JN 25 cm JL 50 cm KN 13 cm KM 26 cm B ZMJL ZKLJ JM LK C JM JK KL LM D ZMJL ZMLJ ZKJL ZKLJ E AJKN ALMN O Yes OYes O Yes Yes O Yes O No O No O No O No O No M N K L

metry 23 Hanna Anguiano CA Geometry B Illuminate Credit 1 pdf According to Theorem 2 label the parallelogram with the appropriate tick marks IIf 1 According to Theorem 3 label the parallelogram appropriately I B If then the quadrilateral is a parallelogram B 00 Regist C According to Theorem 4 label the parallelogram with the appropriate tick marks then the quadrilateral is a parallelogram then the quadrilateral is a parallelogram 1

try 23 Hanna Anguiano CA Geometry B Illuminate Credit 1 pdf 3 2 a 2 4 and b 9 7a 106 16 9b 25 x 6 and y 3 5 2x 2 6y 1 M 20 12 8y 6 4x 10 I

y 23 Hanna Anguiano CA Geometry B Illuminate Credit 1 pdf Your Turn Show that each quadrilateral is a parallelogram for the given values of the variables Step 2 is done for you 1 z 11 and w 4 5 Step 1 Find LF and LH So mZF m and mZE m 9z 19 12w 8 Step 2 Find LE and LG 14w 1 11z 3 LE 12 4 5 8 54 8 EFGH is a parallelogram since 62 LG 14 4 5 1 63 1 62 H 100 G

nit 1 Quadratics choose option A or B Option A 1 Design an experiment to collect data that can be modeled as a parabola 2 Graph the data you obtain from your experiment 3 Determine the equation that best fits the data and graph that as well 4 State the following information based on your graph a the roots b the axis of symmetry c the optimal value