Geometry Questions

25 At 2 P M the shadow of a lighthouse is 19 feet long and the angle of elevation is 75 degrees Find the height of the lighthouse Draw a diagram to illustrate the problem Label the lighthouse shadow and angle of elevation

21 Find the area of an equilateral triangle that has side lengths of 20 centimeters Hints A bh An equilateral triangle is also equiangular Draw a sketch

Matching You will use 2 of the choices twice 1 2 sin R 3 tan R 5 cos R 4 sin S 6 cos S tan S B C D 20 29 21 20 20 21 A 21 29 S 40 T 58 42 F

16 Given cos 0 0 8824 what is the measure of the angle 0

21 Find mzC AB 15 cm BC 8 cm A

20 You decide to measure the height of the stadium lights on the Comets football field The angle of elevation from the ground where you are standing is 32 You are standing 15 meters away from the light post How tall is the stadium light post Draw the figure

1 A tower casts a shadow that is 60 feet long when the angle of elevation of the sun is 65 How tall is the tower

13 11 JM C mZJ ZM 8 X M

24 Find the area of the triangle A bh 11 m 407

23 cos 50 sin

15 Find the measure of both acute angles in the diagram shown B 7m 14 m

12 AB B X A m B m T 27 32 T

22 sin 38 cos 0

Matching 8 9 10 sin A cos A tan A A 1 875 B 0 8824 C 0 4706 A 8 17 15 B

A 12 3x 18 9 A If AABC is similar to ADEF determine the measure of ZA B C 16 22 8 33 4x 2 C D 6 F

14 In the figure below the two triangles are similar AABC AXZY What is tan X 28 A 45 32 B

18 A flagpole casts a shadow that is 19 ft long The angle of elevation from the shadow to the top of the Flagpole is 35 Find the height of the flagpole

11 AB AC X m A 11 35 C

7 Multiple Choice Which ratio is equivalent to sin 32 A cos 32 B sin 58 C cos 58 D tan 3

H Identify the similarity ratio between Quads QRST and Quad PJKO Side lengths from Quad QRST Corresponding Side lengths from Quad PJKO Simplified Ratio of Corresponding Side Lengths RS ST TQ QR JK RS JK ST TQ QR II The similarity ratio of Quad QRST to Quad PJKO is

Question 10 A lamppost is 6 feet high and casts an 8 foot shadow At the same time of day a flagpole near the lamppost casts a 20 foot shadow Using the properties of similar triangles find the height H of the fla H 20 ft A B C D 2 4 ft 15 ft 20 ft 6 ft 26 67 ft 8 ft

Correspo F The pair of figures below is similar Color code corresponding vertices and write the similarity statement 9 R 6 Q 15 S 12 ZQ corresponds to ZR corresponds to ZS corresponds to 2T corresponds J 10 K 15 P 25 20 Quad QRST G Using your similarity statement identify corresponding angles and sides Corresponding Angle Pairs Corresponding Side Pairs RScorresponds to STcorresponds to TQ corresponds to QR corresponds to

Find the length of RQ 25 S

Which of the following is true O A B O C JW QA JB QK BW KQ JB KA BW KA JW KA

B A E Which statements show that A ABE is similar to A ACD Select TWO that apply LABELC A A B C D C D ZA ZC 90 2C LD LABE ZAEB 4 38 and C 38

P B C Q Who is correct and why are they correct A D N M Justin is correct because only one pair of angles can be proven congruent and only one pair of sides can be proven proportion Justin is correct because only one pair of angles can be proven congruent Patrice is correct due to SAS similarity Patrice is correct due to AA similarity

Question 7 Use the figure below to answer the following question C B A AE Given AD BE which of the following justifies A AEB A DEC EC O O O O A E B Definition of Similar Triangles SAS Similarity Theorem C AA Similarity Postulate D Triangle Proportionality Theorem

J 12 P OOO0 14 A 8 B C C K 15 18 6 L 21 9 R

T 12 W 8 D X A B D 24 16 18 12 V Yes the triangles are similar with a scale factor of No the triangles are similar with a scale factor of of No the triangles are similar with a scale factor of 32 No the triangles are similar with a scale factor of 23

C C Which set of transformations maps A ABC to A DEC and support Omar s thinking A B C A D a rotation of 180 clockwise about point C followed by a dilation with a center of point C and a scale factor of 2 a rotation of 180 clockwise about point C followed by a dilation with a center of point C and a scale factor of 1 1 201 a rotation of 180 counter clockwise about point C followed by a dilation with a center of point C and a scale factor of 3 a rotation of 180 counter clockwise about point C followed by a dilation with a center of point C and a scale factor of

Question 1 Examine the properties listed below Determine which of the following properties are true for all parallelograms Select three that apply A four right angles diagonals bisect each other B C D E opposite sides are congruent opposite angles are congruent diagonals intersect at right angles

5 A B S 0 5 C F D E xt X Question 13 Read the question and type your response in the box provided You automatically Find the area of polygon ABCDEFG The area of polygon ABCDEFG is ur

72 Figure Rhombus FGHI H Question 10 Read the question and enter your response in the box provided Use the tools and your keyboard to construct your response What is the measure of ZIHJ ZIHJ What is the measure of ZFGH ZFGH

Find the length of the unknown side of the triangle 12 ft 3 ft The length of the unknown side of the triangle is Simplify your answer Type an exact answer using radicals as needed

A 5 B G 0 5 F D E S Question 12 What shapes can help you find the area of the composite figure A Triangle B Oval C Rectangle D Kite E Trapezoid Yes Yes Yes Yes Yes No No No No No

L Parallelogram Parallelogram Evaluate the student s work and determine if the student used the most specific name possible Rhombus D Rhombus A Select Yes if it is a parallelogram OR Select No if a rectangle would be more specific B Select Yes if it is a rhombus OR Select No if a square would be more specific C Select Yes if it is a rhombus OR Select No if a square would be more specific Select Yes if it is a parallelogram OR Select No if a rectangle would be more specific Yes Yes Yes Yes 2 2 2 2

A 8x 9y 9 Figure Parallelogram ABCD B 10y 2 x 9 Question 7 Determine whether the figure is a parallelogram for the given values of the variables x 9 and y 11 Quadrilateral ABCD is a parallelogram

B Figure Parallelogram ABCD 4x 6 in A y 10 in E 6y in C 3x in D Question 6 Read the question and enter your response in the box provided Use the tools a keyboard to construct your response Use Parallelogram ABCD to find each measure AC inches

Examine parallelogram ABCD below 9y 2 A B C B D 8x6 5x 12 D In order to determine the length of each side of the parallelogram which of the following equations would need to be used Select two that a A 5 12 8r 6 180 C 7y 4 9y2 7y 4 180 5 12 8 6 9y2 7y 4

Question 8 Read the question and enter your response in the box provided Use the tools and your keyboard to construct your response Find the measure of ZZ in order for quadrilateral WXYZ to be a parallelogram Z W 6a 10 186 11 9b 2 mZZ 8a 4 Y X

17 If ASRY AWXQ RT is an altitude of ASRY XV is an altitude of AWXQ RT 5 RQ 4 QY 6 and YX 2 fin XV W T X Q A

Question 2 Which of the following quadrilaterals is NOT a parallelogram A B C D square rhombus rectangle trapezoid

D Which type of shape could quadrilateral ABCD be Select ALL that apply A B C H D square rhombus rectangle parallelogram

11 12 15 ANSWER 13 18 ANSWER 12 30 eSolutions Manual Powered by Cognero 1 7 5 Parts of Similar Triangles 20 15 28 ANSWER 6 27 5 24 a

and the value of x that makes APGH AJKL Lesson 11 3 1 point X 3 5 20 6 The two triangles below are similar What value of Q and B would make this true To solve this problem use the value of x to find the measure of Q and B Lesson 11 3 1 point Learning Goal from Lesson 11 4 I can apply the properties of similarity transformations to establish the AA criterion for two triangles to be similar 7 Using a proportion based on similarity find the length of DE 1 point 9m 13 5 m C B I got it 39 22 5 m 91 98 15x 64 42 How I Did Circle one 4x 2 Q I m still learning it

5 3 1 Find the missing length using the Geometric Mean Theorem 1500 HW 900 T 64 25 X Homework O Complete problems 1 6 below for independent practice When you are finished check the solutions with your teacher 16 ent Practice 36 2 6 580 400 960 576 144 X X 25 x Optional Complete problems 2 5 11 19 20 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

In AQRS QT 5 ft and TS 2 2 ft What is RT Round to the nearest hundredth Lesson 12 4 1 point R T S

Lesson 12 4 Checkpoint Once you have completed the above problems and checked your solutions complete the Lesson Checkpoint below Complete the Lesson Reflection above by circling your current understanding of the Learning Goal 1 Use the Geometric Mean Theorem and your knowledge of proportions to find the value of x K 16 X 20 12

Learning Goal from Lesson 12 1 I can prove two theorems using triangle similarity the theorem that a line parallel to one side of a triangle divides the other two proportionally and the Pythagorean theorem 8 In AAEB CD is parallel to AB Complete each proportion 1 point E a b SRZ 5 ft C d EC CA EC EA EB ED DB EB Learning Goal from Lesson 12 3 and 12 4 I can prove theorems about geometric figures using triangle congruence and similarity 12 ft 6 ft n A 9 The triangles below are similar What is the area of the larger triangle Lesson 12 3 1 point 10 ft 28 ft 20 ft How I Did Circle one I got it B How I Did Circle one I got it I m still learning it 10 Ryan is 6 feet tall At a certain time of day he casts a shadow that is 12 feet long At the same time a tree casts a shadow that is 28 feet long What is the height of the tree Lesson 12 3 1 point I m still learning it

1 Find x 5 X lifelong 7 Z Geometry B Credit 2