Geometry Questions

opposite adjucent spolenice 2 Your Turn 1 Statements 1 LN NP 2 LM 20 3 LLNM LPNO Choose from the phrases in the reason bank above to complete each proof Given LN NP and 2M 20 Prove A LMN A PON 4 ALMNA PON Reason Bank Vertical Angles are Congruent Statements 1 LT LR 2 LSQT LSQR Given 2T LR and ZSQT ZSQR Prove A QTSA QRS 3 QS QS 4 AQTS AQRS Reflexive Property of Congruence Reasons signat T 2 Given Reasons So no AAS Triangle Congruence Theorem M SORP N S O R EXPLAIN

Use the figure to find the value of x 3x 1 E 2x

urements Communicate effectively based on purpose task and audience using appropriate academic vocabulary and medium Angle vence ENGAGE Transformations and Angles Complete the following activity with your teacher in order to continue your learning on lines angles and triangles For triangle ABC the points D E and F are the midpoints of each side of the triangle Use a straightedge to roughly sketch the perpendicular bisector for sides AB BC and AC Name the point where the lines intersect 0 B D ob B E A anothe F For the following triangle ABC use a straightedge to sketch the angle bisectors for each of the angles Locate the location where the lines intersect Hint Simply draw a perpendicular line from these points C Hint Bisect LA LB and C

Write a two column proof 1 Given GJ GM GK bisects ZJGM Prove AGJK AGMK J M K Statement Rea

4 Given ZQ S ZTRS RTQ Prove AQRT ASTR Q T R S Statement Reason

4 Given ZQ ZS ZTRS ZRTQ Prove AQRT ASTR R Statement Reaso

B Prove ABDH AFDH D DH bisects ZBDF 12 H F Statement Reason

lumn proof Given GJ GM GK bisects ZJGM Prove AGJK AGMK J G M K Statement Reason

8 Given ZI 22 DH bisects ZBDF Prove ABDH AFDH B D 12 H F Statement Reason

Write a two column proof 1 Given EF FH ZE H Prove HG DE D G E F H Statement Reason

4 Given ZQ ZS ZTRS ZRTQ Prove AQRT ASTR R Statement R

7 Given ZG ZT I is the midpoint of HV Prove ZH ZV H G T V Statement Reason

5 Given BC CD ZB ZD Prove AB DE A D B C Statement Reason

3 Given ABAC AD bisects ZBAC Prove BEZC A B D C Statement Reason

2 Given BC AD AC BD Prove ZBCD ZADC B D C A Statement Reason

4 Given SP SR Q is the midpoint of PR Prove ZPSQ RSQ P R Statement Reason

3 Given ZK ZM KL ML Prove AJKL APML L J K Statement Reason

of 2 Given AB DC AB DC Prove AABC ACDA A D B C Statement Reason

7 Given ZN ZP MO QO Prove AMON AQOP M Q O N P Statement Reason

Write a two column proof 1 Given EF FH ZE ZH Prove HG DE D G E F H Statement Reason

6 Given GHK ZJHK ZGKH ZJKH Prove AGKH AJKH G K J Statement Reason

the object and the image congruent or not con Explain your answers The diagram shows triangle B on a coordinate grid Make four copies of the diagram On different copies of the diagram draw the image of B after each combination of transformations a b C d 5 1 followed by reflection in the x axis Translation Rotation of 180 centre 3 2 followed by reflection in the x axis Translation 3 5 clockwise centre 2 1 followed by rotation 90 Reflection in the line y 1 followed by rotation 90 anticlockwise centre 2 2 Think like a mathematician 6 5 4 3 2 B 6 5 4 3 2 1 2 3 4 5 6

0 157 1 65 0 0108 0 0028 Z 0 157 1 65 0 0108 0 0028 1 1 solving for T The equation 1 is in quadratic form solving for by evaluating the roots of the quadratic equation Rewring the equatin 1 3 Solving for root Z 1 2 concentration Discarding the negative root 0 06 0 0 0556 0 05 0 04 0 03 0 02 0 82572 0 157 0 008 0 0 04315 0 01 ax bx c 0 T 0 root 0 root T 0 03 b b 4 a c 2 a 0 15 0 152 4 0 825 0 008 2 0 825 0 15 0 0225 0 0264 2 0 825 0 5 0 15 0 2211 2 0 825 1 0 4311 Distance Z 1 5 y 0 0128x 0 0557 R 0 9998 2 2 5

Design a relational schema and SQL quenes to iStore the basis functional dependencies i Check Fa functional dependency is part of the closure of besis set of functional dependencies stored in your relations designed above

Step 1 We want to find the exact value of sin From the text the quadrants are numbered counter clockwise from the upper right I II III IV This angle lies in quadrant III III K T sin 27 Step 2 Sketching the angle we draw the triangle formed with the terminal side and the x axis Looking at this triangle we see triangle that it is a 71 632 2 2 To find that value we first have to draw the angle 3 y Likewise the opposite side should be labeled 2A 3 From the text we know that the side lengths are 1 2 3 To label the sides with the proper lengths we note that 2 being the longest side length must be the hypotenuse The smallest angle will be opposite the shortest side Looking at the triangle and taking into account the quadrant so that the sign is correct the adjacent side should be labeled 3 x

Match each function with its graph 1 f x y 4e 1 x y 3 f x y x 2y 3 42 f x y 4 f x y y 5 f x y x sin y You can drag the images to rotate them Z 1 00 2 00 3 00 1 50 1 50 Z 2 25 4 5 65 A 1 50 Y Z 3 00 2 00 1 00 X5000 B 1 00 6950 1 50 0 00 Y Z 18 00 3 00 5 00ROOY C

Match each function with its graph 1 f x y 3 x y 2 f x y 3 x y 3 f x y 3 cos 4 3 2 4 f x y 1 2 y You can drag the images to rotate them Z 2 25 1 50 X 52 Z 2 25 1 50 0 75 X603 149 A 1 490 00 149 Z 0 75 1 5 3 B

Step 1 We want to find the exact value of sin 3r From the text the quadrants are numbered counter clockwise from the upper right I II III IV This angle lies in quadrant 111 III 11 4 3 To find that value we first have to draw the angle Step 2 Sketching the angle we draw the triangle formed with the terminal side and the y axis Looking at this triangle we see that it is a triangle xxx Likewise the opposite side should be labeled 3A From the text we know that the side lengths are 2 2 2 To label the sides with the proper lengths we note that 2 being the longest side length must be the hypotenuse The smallest angle will be opposite the shortest side Looking at the triangle and taking into account the quadrant so that the sign is correct the adjacent side should be labeled

ind D the value of x 75 5x 10 21 120 I 3x 22 105 x 2

Find 14 the 40 75 values of to 15 106 16 y

3 2 For use with pages 153 160 Find the values of x and y 11 110 12 13 95 to 2011 S

A straight kite string makes an angle of 40 with the ground as shown in the diagram 40 If y 200 feet of string has been let out how high in ft is the kite Round your answer to one decimal place ft Nood Hein

Find the value of x 17 80 x 15 18 farf 68 2x 19 2x 4 92

Find m 1 and m 2 5 60 1 6 120 7 80 2

Find 8 mi 1 and M22 56 2 9 10 117 2 2 108

For use with pages Find the angle measure Tell which postulate or theorem you use 1 If m1 50 then m 5 2 If m 4 45 then m26 3 If m 2 130 then m 7 4 Ifm 6 123 then m 3 2 3 4 519 7 6 8

3 Solve the triangle below Round each answer to the nearest tenth 24 a C 36 16

4 A pilot is flying over a straight highway He determines the angle of depression to two mile posts 2 1 km apart to be 25 and 49 as shown in the figure below Find the distance of the plane from point A and find the elevation of the plane 125 49 A B

r 8 Give two other polar coordinate representations of the point one with r 0 and one with r 0 2 2 3 smaller r value r 0 Need Help Read It 2 X 0 larger r value 2 0

2 y 113 b 10 c 32

For the following exercises assume a is opposite side a is opposite side b and is opposite side c Solve each triangle if possible Round each answer to the nearest tenth 1 B 50 a 105 b 45

7 Given quadrilateral TRAP with T 5 7 R 3 4 A 9 5 and P 1 10 Show TRAP is an isosceles trapezoid 3 4

6 Given AFUN with F 4 1 U 5 6 and N 1 3 Show AFUN is an isosceles right triangle righT ANgle 41 5 6 113

Find all of the solutions to the equation in the interval 0 2 2 sin r1 esc z

Find the standard form of the equation of the hyperbola with the given characteristics Vertices 3 5 3 11 Asymptotes y x 6 y x

Find the center vertices and foci of the hyperbola y 3 x 4 x 4 9 center x y vertices x y foci x y x y x y 1 smaller y value larger y value 2 smaller y value Find the asymptotes of the hyperbola Enter your answers as a comma separated list of equations 4 larger y value Sketch its graph using the asymptotes as an aid Use a graphing utility to verify your graph y 8 6 4 2 2 X 6 8 X X 2 6 4 2 2 4 2 8 8 X

Consider the following 4x 9y 24x 90y 198 0 a Find the standard form of the equation of the hyperbola If the hyperbola is degenerate enter NONE b Find the center vertices foci and asymptotes of the hyperbola If the hyperbola is degenerate enter NONE in each answer blank Center Vertices Foci Asymptotes y negative slope positive slope c Select the correct graph of the hyperbola using the asymptotes as an aid Use a graphing utility to verify your answer A 4 10 6

9 Given APQR with P 1 4 Q 3 0 and R 2 3 Prove APQR is NOT a right triangle 11 1 4 R 2 3 W Q 3 0 Mainita com

Find the standard form of the equation of the hyperbola with the given characteristics Foci 5 0 asymptotes y x

Given ZRUY 90 and ZRST 90 Find YT A R 32 U 46 A Y