3.1 assignment · 3.1 assignment i. order the angles a) least to greatest b) greatest to least c)...

Name: _____________________________________ Date: _____________________ Bell: _______ Geometry Quarter 2 Make Up Work

3.1 Assignment I. Order the Angles

a) least to greatest b) greatest to least c) Order MNO from greatest to least if

MN = 4, NO = 12, and MO = 10

II. Order the Sides

a) least to greatest b) greatest to least c) Order ABC from least to greatest with

mA = 99°, mB = 43°

III. Can a triangle have sides with the given lengths? If so, classify the triangle as acute, obtuse or right.

a) 8 cm, 7 cm, 9 cm b) 7 ft, 13 ft, 6 ft c) 9 in., 12 in., 15 in. d) 5 m, 11 m, 7 m

IV. Given the two sides of a triangle, determine the range for the third side.

a) 5, 11 b) 12, 12 c) 25, 10

Which are possible sides? 5, 10, 15, 18, 26, 34, 35, 38, 40


V. Order the sides

a. List the sides in order from longest to shortest in PQR, with mP = 45°, mQ = (10x + 30) °, and mR = 5x°.

b. List the sides in order from shortest to longest in ABC, with mA = 80°, mB = (3x + 5) °, and mC = (5x − 1) °.

VI. Word Problems

1) Ben, Gilberto and Hannah are playing Ultimate. Hannah is trying to decide if she should pass to Ben or Gilberto. Which

player should she choose in order to have the shorter passing distance? Explain your answer.

2

2) When Toya goes from science class to math class, she usually stops at her locker. The distance from her science

classroom to her locker is 90ft and the distance from her locker to her math class is 110ft. What are the possible

distances from science class to math class if she takes the hallway that foes directly between the two classrooms?

3) Anna, Johnice and Chardan were discussing the triangle below. Anna said that angle M was the smallest, Johnice

thought angle P was the smallest and Chardan argued that angle Q was the smallest. Who was correct and explain why.


3.2 Assignment Ordering Sides of Adjacent Triangles:

Find the shortest side:

Shortest Side: __________

Find the longest side:

Longest Side: ___________

Isosceles Triangles:

What is the measure of

𝑚∠𝑇 = _______________

𝑚∠𝑈 = _______________

Solve for x:

𝑥 =____________

What is the 𝑚∠𝑆 = _______________? Find x.

If 𝑚∠2 = 13𝑥 + 3, what is the value of x?


Special 45-45-90 Isosceles Right Triangles:

𝑥 =__________ 𝑦 =__________

𝑥 =__________ 𝑦 =__________

𝑥 =__________ 𝑦 =__________

Exterior Angles of Triangles:

Find the value of x.

Find the value of x.

Find the 𝑚∠𝐴: _______


3.3 Assignment I. Use the Pythagorean Theorem to find the hypotenuse. Then, use trigonometric ratios to help set up the

proper proportions for the given angle.

a) Angle A:

sin A= _________ cos A= _________ tan A= _________

II. Use trigonometric ratios to help solve for the missing side. Round the nearest tenth.

a) b) c)

d) e) f)


III. Word Problems

3) The measure of the angle of elevation of the sun is 32° when a building casts a shadow 350 feet long. How

tall is the building?

4) A ladder is leaning against a tree. If the foot of the ladder is 9 feet from the base of the tree and makes a

60° angle with the ground, how high up the tree does the ladder go?

Review:

1) What is the range of the third side if two 2) What is the 𝑚∠𝐶𝐵𝑊? ____________

sides are 15 and 32?


3.4 Assignment For questions 1-4, find the measure of the angle.

1) __________

2) __________

3) __________

4) __________

For questions 5-8, find the missing side.

5) __________

6) __________

7) __________

8) __________

For questions 9-11, sketch a picture and then solve.

9) The angle of elevation from a kicker’s foot on the football field to the top of the goal post bars is 17°. If he is standing 131 feet from the base of the goal post, how tall is the goal post? Sketch: Work: 10) A surfer is riding a 7 foot wave. The angle of depression from the surfer to the shoreline is 10°. What is the distance from the surfer to the shoreline? Sketch: Work: 11) Kurt spots a bird sitting at the top of a 40 foot tall telephone pole. If the angle of elevation from the ground where he is standing to the bird is 59°, how far is Kurt standing from the base of the pole? Sketch: Work:


Review:

12) Order the sides from shortest to longest.

13) Order the angles from greatest to least.

14) What is the possible range of the third side for the

following triangle?

15) What is the 𝑚∠𝑁𝑊𝑀?___________

16) Determine if the segment lengths will form a

triangle. If they do, classify the triangle as acute, right or

obtuse.

3√2, 4, 7

17) Find x.

18) The angles of 𝛥𝐴𝐵𝐶 are 𝑚∠𝐴 = 70°, 𝑚∠𝐵 = (4𝑥 + 30)°, and 𝑚∠𝐶 = 6𝑥°. Order the sides from largest to smallest.


Unit 3 Test Review

3) The angles of Δ𝑨𝑩𝑪 𝒂𝒓𝒆 𝒎∠𝑨 = 𝟕𝟎°, 𝒎∠𝑩 = (𝟒𝒙 + 𝟑𝟎)°, 𝒂𝒏𝒅 𝒎∠𝑪 = 𝟔𝒙°. Order the sides from largest to smallest. Answer: __________ , ___________ , ____________

4)

5) Which of the following triangles are right triangles? 6) Side lengths 2√𝟐, 3, and 𝟐 will form a…. a) right triangle b) obtuse triangle c) acute triangle Show work to justify your answer

7) Solve for x.

𝒂) 𝟏𝟗 𝒃) 𝟏𝟖𝟏 𝒄) √19 𝒅) √181

8) 8)


9) Select the appropriate formula to find the measure of x in the triangle below. A) 𝐬𝐢𝐧−𝟏 ( 𝟕 𝟏𝟏) B) 𝐜𝐨𝐬−𝟏 ( 𝟕 𝟏𝟏) C) 𝐭𝐚𝐧−𝟏 ( 𝟕 𝟏𝟏)

10) A kite is flying at a height of 40 feet. Its angle of elevation is 52 degrees. What is the length of the kite string, rounded to the nearest tenth of a foot? ________________

11) Find x. ________ Round to the nearest tenth. 12) The perimeter of the square below is 48 cm. Find the approximate length of the diagonal. Round your answer to the nearest tenth.

13) Find x. ______ 14) A 20-ft ladder is leaning against a house. What is the distance between the bottom of the ladder and the bottom of the house?

A) 𝟏𝟎√2 B) 𝟒𝟎 C) 𝟏𝟎

D) 𝟏𝟎√𝟑

15) Which is the shortest side?

16) While parasailing, Ryan spots a dolphin on the water below. If Ryan is 228 feet above the water and the angle of depression to the dolphin is𝟏𝟓°, what is the horizontal distance between Ryan and the dolphin? Sketch: Work:


1. Given: Parallelogram GTUS with ST = 10 and GM = 4.

a) MT = __________

b) GU = ____________

2. Given: Rhombus VREA, VL = 8 and LR = 6.

a) VR = ___________

b) Perimeter of VRAE = ___________

4. Given: Rectangle MATH, with AH = 13 and MH = 5.

a) MA = __________

b) MT = __________

3. Given: Rhombus MATH, AH = 24 and MT = 32.

a) HG = ___________

b) MA = ___________

4.1 Assignment


𝑚∠ 1 = _______ 𝑚∠ 2 = _______

𝑚∠ 3 = _______ 𝑚∠ 4 = _______

7. Given the rhombus below,

find the measures of the numbered angles.

8. Given the rhombus below,

find the measures of the numbered angles.

𝑚∠ 1 = _______ 𝑚∠ 2 = _______

𝑚∠ 3 = _______ 𝑚∠ 4 = _______

9. Given: Square MATH with perimeter = 80.

a) MT = __________ b) GH = __________

10.

5. Given Parallelogram JKLM, where 𝒎∠𝑲𝑱𝑳 = 𝟒𝟕°,

𝒎∠𝑲𝑳𝑵 = 𝟐𝟓° and 𝒎∠𝑲𝑵𝑳 = 𝟓𝟔°. What is the

𝒎∠𝑲𝑱𝑴? ______

6. Given Isosceles Trapezoid RSTU with bases RS and

TU.

Sketch:

𝑆𝑇̅̅̅̅ ≅ __________ 𝑅𝑇̅̅ ̅̅ ≅ __________


!!!!!!!!!!!

!

!!!

!!!

!!!

!!!

!!!!

Find!the!4th!vertex!of!the!parallelogram!below,!in!the!specified!quadrant.!

PARALLELOGRAMS

- opposite sides are parallel

- opposite sides are congruent

- opposite angles are congruent

- consecutive angles are supplementary

- diagonals bisect each other

4. 3)

4.2 Assignment 1) Given the rectangle ABCD below, find the value of x and the 𝒎∠ 𝑨𝑪𝑫.

𝑥 = _________ 𝑚∠𝐴𝐶𝐷 = _________

Justification: _______________________________

For 2-3, Given the parallelograms below:

Justification: _______________________________ Justification: _______________________________

4) Given Rectangle PQRS with 𝑹𝑷 = 𝟕𝒙 + 𝟔 and 𝑺𝑸 = 𝟏𝟖. Find x.

𝑥 = __________

Justification: _______________________________

5) Given Rectangle PQRS, with 𝑺𝑻 = 𝟐𝒙 + 𝟔 and 𝑷𝑹 = 𝟐𝟎. Find x.

Justification: _______________________________ 𝑥 = __________

6) Given Isosceles Trapezoid VINE with 𝑬𝑰 = 𝟗𝒙 + 𝟓 and 𝑽𝑵 = 𝟑𝒙 + 𝟒𝟏. Find the length of each diagonal.

Justification: _______________________________ 𝐸𝐼 =______ 𝑉𝑁 = ______

7) In Square ABCD, 𝑨𝑪 = 𝟑𝒙 − 𝟒 and 𝑩𝑬 = 𝒙 + 𝟔, where E is the intersection of the diagonals. What is the length of AC?

𝑥 = _________ 𝐴𝐶 = _________

Justification: _______________________________

2)


8) Given Rhombus QRST, find the value of x and the 𝒎∠𝑹𝑺𝑻.

𝒙 = _________ 𝑚∠𝑅𝑆𝑇 = _________

Justification: _______________________________

9) Find the coordinates of the midpoints of the diagonals of the following quadrilaterals.

a) b)

Work: Work:

Midpoint of AC: __________ Midpoint of AC: __________

Midpoint of DB: __________ Midpoint of RB: __________

c) Based on your findings which of the above examples is a parallelogram? How do you know?

10) Find the length of FH and GJ.

𝐹𝐻 =__________

𝐺𝐽 =__________

11) X-braces are used to provide

support in fencing. If 𝑨𝑩 = 𝟔ft, 𝑨𝑪 =

𝟐ft, and 𝒎∠𝑪𝑨𝑬 = 𝟔𝟓, find each of

the following:

a) BD= _______ b) CB=______

c) 𝑚∠𝐷𝐸𝐵 = _______

d) 𝑚∠𝐸𝐶𝐷 =_______

12) ABCD is a rhombus. If 𝐸𝐵 =9, 𝐴𝐵 = 12 and 𝑚∠𝐴𝐵𝐷 = 55°, find each measure. a) 𝐴𝐸 =_______ b) 𝐶𝐸 =________

c) 𝑚∠𝐵𝐷𝐴 = _______

d) 𝑚∠𝐴𝐶𝐵 =_______


4.3 Assignment

Determine if the following quadrilaterals are parallelograms. Explain your reasoning.

1) 2) 3)

Complete the following two column proofs. Use the Answer Box at the bottom of the page for both proofs.

4) Given: Parallelogram JKLM, 𝒎∠𝑴 = 𝟔𝟓°

Prove: 𝒎∠𝑲 = 𝟔𝟓°

5) Given: PQRS is a parallelogram, 𝑷𝑺 ≅ 𝑸𝑻

Prove: ∆𝑸𝑹𝑻 is an isosceles triangle.

Statement Reason

1) Parallelogram JKLM

2) 𝑚∠𝑀 = 65°

3) 𝑚∠𝑀 = 𝑚∠𝐾

4) 𝑚∠𝐾 = 65°

Statement Reason

1) PQRS is a parallelogram

2) 𝑄𝑅 ≅ 𝑃𝑆

3) 𝑃𝑆 ≅ 𝑄𝑇

4) 𝑄𝑅 ≅ 𝑄𝑇

5) ∆𝑄𝑅𝑇 is an isosceles triangle.

Answer Bank:

a) Opposite sides are congruent b) Opposite sides are parallel c) Opposite angles are congruent

d) Opposite sides are supplementary d) Opposite angles are supplementary

e) Same Side Interior Angles are supplementary f) Given g) Prove h) Substitution Property

i) Transitive Property j) Definition of an Isosceles Triangle

k) Definition of an Isosceles Trapezoid


6) Find the missing endpoint M if point K is the midpoint of 𝑳𝑴̅̅̅̅̅.

a) L(-9,-4) and K(2,-1) b) K(-4,-6) and M(-7,-3)

Review

7) Given rectangle RSTU, 𝑺𝑻 = 𝟏𝟓 and 𝑼𝑺 = 𝟐𝟓. Find the perimeter of the figure.

Sketch: Work:

Perimeter: __________

8) Given Parallelogram DEFG. If 𝑭𝑯 = 𝟏𝟏 and 𝑭𝑫 = 𝟒𝒙 + 𝟐, what is the value of x?

x=__________

9) Given Rhombus ABCD. Find the perimeter of the figure is 𝑨𝑪 = 𝟏𝟎 and 𝑩𝑫 = 𝟐𝟒.

Perimeter:__________

10) Find all the missing angles of Rhombus STUV:

𝑚∠1 = _______ 𝑚∠2 = _______

𝑚∠3 = _______ 𝑚∠4 = _______

𝑚∠5 = _______ 𝑚∠6 = _______

𝑚∠7 = _______

11) Given Parallelogram ABCD. Complete each statement and write a justification for each answer.

a) 𝐴𝐸 ≅ ___________ ____________________________________

b) ∠𝐴𝐵𝐶 ≅ ___________ ____________________________________

c) 𝐷𝐴̅̅ ̅̅ || __________ ____________________________________

d) 𝐷𝐶̅̅ ̅̅ ≅ __________ ____________________________________

e) ∠𝐵𝐴𝐷 + ∠𝐶𝐷𝐴 =__________ _______________________________________


Unit 4 Test Review

Given the following parallelograms:

1a) What is the 𝑚∠𝑊𝑌𝑍? __________

1b) What is the 𝑚∠𝑅𝑈𝑆? __________

2a) The 𝑚∠𝐺𝐹𝐾 = 35°, the ∠𝐺𝐻𝐹 = 40° and the 𝑚∠𝐽𝐾𝐻 =

72°. What is the measure of the following angles?

𝑚∠𝐻𝐽𝐾 =________

𝑚∠𝐽𝐻𝐺 = ________

2b) The 𝑚∠𝑇𝑊𝑋 = 43°, the ∠𝑋𝑌𝑊 = 49° and the

𝑚∠𝑊𝑇𝑍 = 72°. What is the measure of the following

angles?

𝑚∠𝑋𝑇𝑌 =________

𝑚∠𝑊𝑋𝑌 = ________

3a) 𝐹𝐻 = 14 and 𝐺𝐾 = 6. What is 𝐻𝐾 + 𝐺𝐽?______

3b) 𝑊𝑇 = 7 and 𝑍𝑋 = 10. What is 𝑌𝑊 + 𝑋𝑇? _______

Given the following rectangles:

4a) If the 𝑚∠𝐷𝐴𝐸 = 32°, what is the 𝑚∠𝐴𝐵𝐷? ______

4b) If the 𝑚∠𝑅𝑉𝑆 = 102°, what is the 𝑚∠𝑅𝑈𝑉? ______

5a) Given Rectangle JKLM, if 𝐽𝐾 = 12 and 𝑀𝐾 = 15, what is

the perimeter of the rectangle?

5b) Given Rectangle TUVW, if 𝑇𝑊 = 8 and 𝑇𝑉 = 17, what is

the perimeter of the rectangle?

6a) If the 𝑚∠𝐴𝐵𝐸 = (3𝑥 + 12)° and the 𝑚∠𝐶𝐵𝐸 = (6𝑥 +

6)°, what is the value of x?

6b) If the 𝑚∠𝑅𝑈𝑉 = (2𝑥 − 7)° and the 𝑚∠𝑉𝑈𝑅 = (3𝑥 +

2)°, what is the value of x?

7a) If 𝐴𝐶 = 3𝑥 − 7 and 𝐷𝐸 = 7, what is the value of x?

7b) If 𝑆𝑉 = 4𝑥 + 2 and 𝑅𝑇 = 68, what is the value of x?


Given the following Rhombi:

8a) Find the missing angles:

8b) Find the missing angles:

9a) If 𝑅𝑇 = 12 and 𝑈𝑆 = 16, what is the perimeter?

9b) If 𝐷𝐹 = 60 and 𝐸𝐺 = 32, what is the perimeter?

Given the following squares:

10a) If 𝑉𝑊 = 6, what is the perimeter?

11a) If 𝐺𝐸 = 18, what is the perimeter?

Given the following isosceles triangles:

12a) If 𝑃𝑁 = 5𝑥 + 19 and 𝑀𝑂 = 12𝑥 − 37, what is the value

of x?

12b) If 𝑊𝑈 = 8𝑥 + 3 and 𝑇𝑉 = 4𝑥 + 35, what is the value of

x?

Midpoint:

13a) Given Parallelogram MHSG, at which point will the

diagonals bisect each other?

13b) What is the center point of parallelogram TURN?

14a) What is the coordinate of R, given the midpoint of 𝑅𝑆̅̅̅̅ is

𝑇(−3,6) and 𝑆(−1,9)?

15b) Given 𝐴𝐵̅̅ ̅̅ with a midpoint at 𝐸. If E is located at point

(2, −3) and 𝐵 is located at (−2, 1), at what point must A be

located at?


a) Slope of 𝑀𝐺̅̅̅̅̅ = ______ b) Slope of 𝐻𝑆̅̅ ̅̅ = ______

c) 𝑀𝐺 ≈ ________ d) 𝐻𝑆 ≈ ________

e) Quadrilateral HSGM is a _______________________ because

_____________________________________________________

16a) Prove Quadrilateral MGHS is a parallelogram.

16b) Prove Quadrilateral TURN is a parallelogram.

17a) Determine if the following quadrilaterals are

parallelograms.

17b) Determine if the following quadrilaterals are

parallelograms.

18a) Given the following parallelograms, find x and y.

𝑥 =__________, 𝑦 =__________

18b) Given the following parallelograms, find x and y.

𝑥 =__________, 𝑦 =__________

a) Slope of 𝑁𝑇̅̅ ̅̅ = ______ b) Slope of 𝑅𝑈̅̅ ̅̅ = ______

c) 𝑁𝑇 ≈ ________ d) 𝑅𝑈 ≈ ________

e) Quadrilateral TURN is a _______________________ because

____________________________________________________


Name Class Date

9-2

Practice (continued) Form G

Copy each pair of figures. Then draw the line of reflection you can use to map

one figure onto the other.

15. 16.

Reflections

Name Class Date

9-2

Practice (continued) Form G

Copy each pair of figures. Then draw the line of reflection you can use to map

one figure onto the other.

15. 16.

Reflections

Name Class Date

9-4

Practice Form K

Tell what type(s) of symmetry each figure has. If it has line symmetry,

sketch the line(s) of symmetry. If it has rotational symmetry, tell the

angle of rotation.

1. To start, look for the ways that the figure will reflect

across a line onto itself.

2. Look for a possible center point.

Think about angles formed by joining image-preimage

pairs to the center. All these angles must be ? for a figure

to have rotational symmetry.

3. 4.

5. 6.

Determine how many lines of symmetry each type of polygon has.

Include a sketch to support your answer.

7. equilateral triangle 8. square

9. regular pentagon 10. regular octagon

Prentice Hall Foundations Geometry • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.

35

Symmetry

Name Class Date

9-4

Practice Form K

Tell what type(s) of symmetry each figure has. If it has line symmetry,

sketch the line(s) of symmetry. If it has rotational symmetry, tell the

angle of rotation.

1. To start, look for the ways that the figure will reflect

across a line onto itself.

2. Look for a possible center point.

Think about angles formed by joining image-preimage

pairs to the center. All these angles must be ? for a figure

to have rotational symmetry.

3. 4.

5. 6.

Determine how many lines of symmetry each type of polygon has.

Include a sketch to support your answer.

7. equilateral triangle 8. square

9. regular pentagon 10. regular octagon

Prentice Hall Foundations Geometry • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.

35

Symmetry

5.1 Assignment

Coordinate Geometry: Given points 𝑴(𝟑, 𝟑), 𝑵(𝟓, 𝟐) and 𝑶(𝟒, 𝟒), graph ∆𝑴𝑵𝑶 and its reflection across each line.

1) the y-axis 2) the x-axis

3) 𝑥 = 1 4) 𝑦 = −𝑥

Draw the line of reflection you can use to map one figure onto the other.

5) 6)

Determine if each figure has line symmetry. If it has line symmetry, sketch the line(s) of symmetry.

7) 8) 9)


Perform the indicated translations and write the rule for each.

(x,y) -----------> (_________, _________) (x,y) -----------> (_________, _________)

12) Use the diagram to answer parts a, b, and c.

a) Find the rule to describe the translation from point A to point B.

(x,y) -----------> (_________, _________)

b) Find the rule to describe the translation from point C to point D.

(x,y) -----------> (_________, _________)

c) Find the rule to describe the translation from point E to point A.

(x,y) -----------> (_________, ________)

13) Brittany’s neighborhood is shown on the grid at the right.

a) If she leaves home and travels 4 blocks north and 3 blocks west,

what is her new location?

b) Use words to describe two possible translations that will take

Brittany home from school.

14) Jamil and Ashley are finding the coordinates of the image of (2,3) after a reflection in the x-axis. Is either of them

correct? Explain.

Jamil Ashley

𝐶′(2, −3) 𝐶′(−2,3)


5.2 Assignment

1. Determine how each of the figures was moved. Write translated, reflected, or rotated.

2. Complete the following rotations for the given pre-image around the origin.

a) 90° Clockwise b) 180° c) 270° Clockwise

𝐴(−2,1) → 𝐴′(______, ______) 𝐷(−4,3) → 𝐷′(______, ______) 𝑊(−2,4) → 𝑊′(______, ______) 𝐵(2,4) → 𝐵′(______, ______) 𝐸(1,2) → 𝐸′(______, ______) 𝑋(3,6) → 𝑋′(______, ______) 𝐶(5,2) → 𝐶′(______, ______) 𝐹(−3, −3) → 𝐹′(______, ______) 𝑌(5,2) → 𝑌′(______, ______) 𝑍(0,0) → 𝑍′(______, ______) 3. Given the figure on the left, what possible rotation would be used to generate figures a, b, and c.

a) b) c)

__________________ __________________ __________________

__________________ __________________ __________________

4. Determine if the figures below have point symmetry, line symmetry, both or neither.

a) ____________________ b) ____________________ c) ____________________ d) ____________________


5. Given the congruency statement, list all congruent angles and sides

∆𝐹𝐷𝑇 ≅ 𝑃𝑁𝐶

6. Complete the following congruency statements

a) ∆𝐷𝐸𝐹 ≅ ∆𝐾𝐽𝑃 𝐹𝐷̅̅ ̅̅ ≅ _________ b) ∆𝐵𝐴𝐶 ≅ ∆𝐿𝑀𝑁 ∠𝐴 ≅ __________

c) ∆𝑍𝑋𝑌 ≅ 𝑍𝑋𝐶 ∠𝑍𝑌𝑋 ≅ __________ d) ∆𝑅𝑇𝐻 ≅ ∆𝑆𝐴𝑅 𝑅𝐴̅̅ ̅̅ ≅ ___________

7. Given: ∆𝑩𝑪𝑴 ≅ 𝒁𝒀𝑹

a) 𝑚∠𝐵 = __________ b) 𝐶𝑀 = ___________

c) 𝐵𝑀̅̅̅̅ ̅ ≅ __________ d) 𝑚∠𝑀 = __________

d) ∠𝑌 ≅ __________ e) 𝑌𝑍̅̅̅̅ ≅ __________

5.1 Review:

6). 7) What is the rule of the translation?

(x,y)→ (____________, _____________)

(𝑥, 𝑦) → (____________, _____________)

Angles Sides

3.1 assignment · 3.1 assignment i. order the angles a) least to greatest b) greatest to least c)...

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