Geometry Questions

14 In the following diagram x and y represent adjacent sides of a parallelogram Does x y x Explain A B y D

Does JM bisect J Explain cmpo 15 M

CD bisects C Solve for CA AE 21 8

Does JM bisect J Explain 15 L 5 M 6

symm Jennifer draws the rectangle ABCD Find all rotations and reflections that carry rectangle ABCD onto itself

What is the image of the point 6 2 after a rotation of 90 counterclockwise about the origin

For each figure determine how many lines of reflection and how many angles of rotation will carry the figure onto itself B

What is the image of the point 5 4 after a rotation of 270 counterclockwise about the origin

Follow the guided instructions below to rotate the figure 270 clockwise about th origin Draw a circle centered at the center of rotation such that one of the vertices of the figure is on the circle 10 9 8 7 6 5 4 3 2 1 10 y 9 8 7 6 5 2 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 10 X

Does JM bisect J Explain Nound 15 L 5 M 6

Solve for x 15 2r 4 18 8

Complete the following problems after the mini lesson CD bisects C Solve for CA D 11 22 B

Tyler says that since triangle ACD is similar to triangle ABC the length of CB is 11 96 Noah says that since ABC is a right triangle we can use the Pythagorean Theorem So the length of CB is 12 exactly Do you agree with either of them Explain or show your reasoning AD 5 4 6 13 B

Next draw CD perpendicular to AB as shown in the next figure Label the red triangle as triangle 2 The blue triangle as triangle 3 How many triangles do you see in the figure Why are the three triangles similar to each other

a Determine if each transformation represents a translation rotation reflection or none CC D How I know b A B 7 A How I know B C C A A B B 02 How I know C

Next draw CD perpendicular to AB as shown in the next figure Label the red triangle as triangle 2 The blue triangle as triangle 3

Symmetry For each figure determine how many lines of reflection and how many angles of rotation will carry the figure onto itself B

Triangle 1 green is the original right triangle we started with Triangle 2 red is the other triangle formed by constructing CD Its right angle is angle D By comparing these two triangles we see that Therefore a cp Now let s complete the proof By adding the two equations we will get What do we notice about the side length p q So we can substitute p q for a b cp cq a b c p q By substitution we get a b c

1 3 2 4 8 60 10 7 9 11 5 59 6 m21 m 2 m23 m24 m25 m26 m27 m28 m 9 m 10 m 11

As shown in the figure AABC satisfies ZABC 30 AB 4 take the circumcenter of AABC as the center to make a circle I AABC is within I extend AB to intersect I at D extend BC to intersect I at E if BD 6 CE 5 find the area of T E A B D

as a zero 1 In Geogebra create the following function f x y 2sin x cos y which will plot the surface defined by the function and plot point A for the value in the function s domain The point should be a 3D point on the surface

44 Interpret a government spending multiplier of 7 5 points

Find the exact value of the expression if possible If not possible enter IMPOSSIBLE a cos arc sin b sin arc tan

The likelihood of falling into an alcohol induced coma is highest when consuming Group of answer choices 5 alcoholic drinks in 2 hours a whole 750 mL bottle of whisky in 2 hours a whole 750 mL bottle of beer in 2 hours enough alcohol to raise blood alcohol levels above 0 55

8 Find the area of the region inside r 4 sin but outside r 2

9 Find the slope of the tangent line to the polar curve r when 0

5 A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at 0 degrees from the horizonta Find 0 if F 5 100 pounds and W 14 000 lb Approximate the answer to one decimal place 21 4 22 4 23 4 20 4 19 4

6 Select a value for b such that a triangle with A 59 and a Ob 15 O b 24 O b 16 O b 11 Ob 17 14 has only one solution

28 In the figure a and are positive angles CL a 9 b 18 e 20 e C

19 Find the magnitude and direction angle of v 2i 6j Round the direction angle to the nearest degree O 67 0 279 O v 2 10 0 252 O lv 30 0 239 O v 2 13 0 260 ly l 3 7 A 269

21 Given C 119 B 42 and c 15 use the Law of Sines to solve the triangle for the value of a Round your answer to two decimal places a 7 3 O a 6 81 O a 4 36 O a 19 61 a 5 58

6 To approximate the length of a marsh a surveyor walks 275 meters from point A to point B then turns 76 and walks 245 meters to point C se figure Approximate the length AC of the marsh where a CO a 245 m b 275 m B b A

4 Given A 50 B 74 and c 8 use the Law of Sines to solve the triangle for the value of a Round your answer to two decimal places O O A a 7 39 a 6 38 a 8 66 a 6 9 a B

12 Determine the area of a triangle having the following measurements Round your answer to two decimal place B 84 38 a 7 and c 8 22 30 sq units 27 88 sq units 25 09 sq units 33 45 sq units

17 At what angle A shown below should the support for 0 5000 5 75 4 2 9375 6 5 A 3 0625

In the figure below a 9 b 11 and d 13 Use this information to solve the parallelogram for x The diagonals of the parallelogram are represented by c and d Round your answer to two decimal places X b a 8 ficuno no drawn to gaala

11 Use the Law of Sines to solve if possible the triangle If two solutions exist find both Round your answers to two decimal places A 60 a 13 b 11 6 B 50 6 C 69 40 c 14 05 B 29 C 91 c 13 B 69 40 C 50 6 c 11 6 B 91 C 29 c 14 05

5 Given C 116 a 13 9 and c 9 3 use the Law of Sines to solve the triangle if possible for the value of b If two solutions exist find both Rou your answer to two decimal places b 1 99 and 6 31 b 1 06 and 6 44 b 4 43 not possible b 7 68

Use the law of Cosines to solve the given triangle Round your answer to two decimal places a 9 b 4 5 C 110 b C a B

ladder of length 10 ft has a distance of 6 ft from a wall To what height does the ladder reach wall 10 ft ladder 6 ft O 1 8 ft O 2 60 ft O 3 16 ft 4 4 ft

Consider the following sin 10 cos 0 a Eliminate the parameter to find a Cartesian equation that represents the curve 2 F Cloudy X sin CHOICE A b Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases CHOICE B 0 CHOICE C y 0 0 5 0 5 y 0 2 0 4 0 6 0 8 1 0 y 0 2 0 4 0 6 0 8 TE SOST 1 0 0 5 0 5 Q Search X 1 0 CHOICE D 1 0 0 5 0 5 y 1 0 0 8 0 6 0 4 0 2 0 8 0 6 0 4 0 2 0 5 0 5 1 0 1 0 A

Find the total area of the shaded regions 6 RE 16 x 16x U COB The total area of the shaded regions is Type an integer or a simplified fraction

equation below gives parametric equations and parameter intervals for the motion of a particle in the xy plane Identify the particle s path by finding a Cartesian equation for it Gra Cartesian equation Indicate the portion of the graph traced by the particle and the direction of motion x 5t 6 y 25t o t Find a Cartesian equation for the particle s path 10 y Graph the Cartesian equation below Indicate the direction of motion as t increases Choose the correct graph below OA O C OB 10 10 A TO Q 14 A point s possible This question 4 point s possible Q Indicate the portion of the graph traced by the particle Select the correct choice below and if necessary fill in the answer box to complete your choice A The portion of the graph where t is greater than B The entire graph C The portion of the graph where t is less than OD Sul

10 Consider the function y 3 x 2 8 a State the transformations the b Graph the parent function c Graph the transformed function 1K Show your work in the table below or graph all the transformations on the grid provided In 8

Theorem 3 12 Lines Perpendicular to a Transversal Theorem In a plane if two lines are perpendicular to the same line then they are parallel to each other If m 1 p and n 1 p then m n Notes Extra Practice In Exercises 1 4 find the distance from point A to BC Ay 1 3 3 0 A B 4 B 1 3 2 3 4 A 3 3 4 2 Ay 4 C D 0 1 3 2 D 1 2 4 x 2 C 1 1 4 x Use the distance formula for 1 4 2 4 A 3 4 4 2 4 2 Ay 4 2 2 C 1 4 D 0 4 D 3 2 B 4 A 1 3 C Am n FF 4 1 X 3 2 B 1 2 4 x

In Exercises 5 8 determine which lines if any must be parallel Explain your reasoning 5 6 7 8 p HI p Am Am n n 1 2 S a k t

12 in 45 a 30 b zoom in 4 4 X given this triangle Find a and b given this triangle You can format your answer like a 38 in b 5 13 radical 17 if you cannot find how to enter radicals on your chromebook Include units in at the end of each answer a 5 b 7

7x 15 12 in x 28 4x 3 zoom in 3 Find x given this triangle Find a and b given this triangle You c wer like a 38 in b 5

3 Determine whether the Law of Sines or the Law of Cosine is needed to solve the triangle Then solve the triangle a 8 c 5 B 40 Law of Sines A 102 34 C 37 66 b 5 26 O Law of Sines No solution Law of Cosines A 37 66 C 102 34 b 5 26 Law of Sines A 37 66 C 102 34 b 5 26 Law of Cosines A 102 34 C 37 66 b 5 26

24 Given that KM is the perpendicular bisector JL prove that JK LK 24 Given that KM is the perpendicular bisector of JL prove that JK LK Use the word phrase bank to complete the paragraph proof 1 KM is the perpendicular bisector of JL KML and 2 are both of perpendicular lines KM KM by the Triangle QTR Triangle SRT by the Therefore JK LK because congruent A Reflexive Property B Corresponding C Alternate Interior D Angle Angle Side Congruence E Angle Side Angle Congruence F Side Angle Side Congruence 5 6 4 3 by definition of a bisector G Right H Congruent J KMJ K MLK L JK LK M JM LM Theorem Langles by definition parts of congruent triangles are