honors geometry chapter 1...

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HONORS

GEOMETRY

CHAPTER 1

WORKBOOK

FALL 2016

1

Honors Geometry

Skills Review Worksheet

For numbers 1 – 3, solve each equation.

1. 8x – 2 = –9 + 7x 2. 12 = –4(–6x – 3) 3. –5(1 – 5x) + 5(–8x – 2) = –4x – 8x

For numbers 4 – 6, simplify each expression by multiplying.

4. 2x(–2x – 3) 5. (8p – 2)(6p + 2) 6. (n2 + 6n – 4)(2n – 4)

For numbers 7 – 9, factor each expression.

7. b2 + 8b + 7 8. b2 + 16b + 64 9. 2n2 + 5n + 2

For numbers 10 – 14, solve each equation.

10. 9n2 + 10 = 91 11. (k + 1)(k – 5) = 0 12. n2 + 7n + 15 = 5

13. n2 – 10n + 22 = –2 14. 2m2 – 7m – 13 = –10

For numbers 15 – 18, simplify each radical.

15. 72 16. 80

17. 32 18. 90

2

Honors Geometry

Algebra Skills Practice

I. Solving Linear Equations

1. 2x + 5 = 11 2. 3x + 5 = –16 3. 2(x – 3) = 84

4. 5x – 32 = 80 5. 3(2x + 5) – 3x = 6 6. 3x – 4(x – 4) + 4 = 13

II. Solving Systems of Equations by Elimination.

7. 2 7 3

4 2 18

x y

x y

8. 39

1785

x y

x y

9. 6 4 7

15 12 1

x y

x y

10.

11 3 39

6 12 19

x y

x y

III. Solving Systems of Equations by Substitution

11. 6 2

5 30 10

x y

x y

12. 9 2 6

5 4 12

x y

x y

13. 2 3 8

9 3 14

x y

x y

14.

10 5 3

6 30 81

x y

x y

3

IV. Simplifying Radicals

15. 52 16. 6

10 17.

12

8

18. 5

15 19.

3

3 20.

3 5

20

21. 50

75 22.

16

24 23.

10 10

80

V. Solving Quadratic Equations by the Quadratic Formula

24. x2 – x = 6 25. x2 + 8 = 6x

26. 4x2 = 4x – 1 27. 4x2 – 3x = 7

VI. Solving Quadratic Equations by Factoring (when a = 1)

28. x2 – 2x – 35 = 0 29. x2 – 10x – 24 = 0

30. x2 – 9x = 2x + 12 31. 32x + 240 = –x2

VII. Solving Quadratic Equations by Factoring (when a ≠ 1)

32. 2x2 + x – 3 = 0 33. 24x – 35 = 4x2

34. 7x + 21 = 14x2 35. –72x2 + 36x + 36 = 0

VIII. Solving Special Cases of Quadratic Equations

36. x2 – 3 = 125 37. 45x2 – 586 = 19,259

38. 12x2 + 420 = 40x2 – 1372 39. 4x2 + 5 = 54

40. 5x2 + 5 = x2 + 25 41. 3x2 – 6x = 11x

IX. Solving Radical Equations and Proportions

42. 3 2 5x 43. 5 2 3x

44. 2 1

3

y

y y

45.

8

2 6 15

x x

x

Common Core State Standards –

G. CO. 1 Know precise definitions of angle, circle,

perpendicular line, parallel line, and line segment, based on

the undefined notions of point, line, distance along a line, and

distance around a circular arc.

Learning Targets –

1. Students will be able to identify and model points,

lines, and planes.

2. Students will be able to identify intersecting lines and

planes.

Section 1.1 Notes: Points, Lines, and Planes

Vocabulary Word Definition Picture

Undefined terms

No Picture Necessary.

Provide Examples:

Point

Named by :

Line

Named by :

Plane

Named by :

Collinear Points

Coplanar Points

Example 1:

a) Use the figure to name a line containing point K.

b) Use the figure to name a plane containing point L.

Example 2: Name the geometric shape modeled by a 10 12

patio.

Example 3: Name the geometric shape modeled by a button

on a table.

Example 4: Create a real-life example for a plane.

Example 5: Create a real-life example for a line.

Vocabulary Definition Picture

Intersection

***Two or more geometric figures intersect if they

have one or more points in common.

Example 6:

= b) =

Example 7: Draw and label a figure for the following

situation. Plane R contains lines AB and DE, which intersect at

point P. Add point C on plane R so that it is not collinear with

AB or .DE

Example 8: Draw and label a figure for the following

situation. QR on a coordinate plane contains Q(–2, 4) and

R(4, –4). Add point T so that T is collinear with these points.

Vocabulary Definition Examples

Defined Terms

Space

Example 9:

a) How many planes appear in this figure?

b) Name three points that are collinear.

c) Are points A, B, C, and D coplanar? Explain.

d) At what point do DB and CA intersect?

Honors Geometry Pages 8 – 11: Numbers 15, 18, 36, 44, 46, 58, 59 1.1 Textbook Homework

Common Core State Standards

G.CO.1 Know precise definitions of angle, circle,




G. CO. 12 Make formal geometric constructions with a variety

of tools and methods (compass and straightedge, string,

reflective devices, paper folding, dynamic geometric software,

etc. )

Learning Targets

1. Students will measure segments.

2. Students will be able to calculate with measures.

Section 1.2 Notes: Linear Measure


Line Segment

Named by :

Example 1:

a) Find the length of AB using the ruler.

b ) Find the length of AB using the ruler.


Betweeness of Points

Example 2: Find XZ. Assume that the figure is not drawn to scale.

Example 3: Find LM. Assume that the figure is not drawn to scale.

Example 4: Find the value of x and ST if T is between S and U, ST = 7x, SU = 45, and TU = 5x – 3.


Congruent Segments

Named by :

What symbol is used to indicate congruence?

Example 5: The perimeter of (the distance around) ABCD is 66, and is twice as long as How long is

Given: ,

Draw a picture here!

A B

C D

Linear Measure and Precision Extra Problems

Find the length and precision of each object:

1.

_______________mAB

2.

Length of pencil = ______________

3.

_______________mCD

4.

_______________mEF

5. What does AB = 2.3cm mean?

6. What does 1

14

mCD in mean?

7. If CA BO , and 0.6mCA cm , find BO.

8. If TI ME , and ME = 5

18

in , find mTI .

Find the measure of each segment:

9. AC = ____________

10. ST = ____________

11. WX = ____________

C D

Create a diagram for each problem, solve for the missing values.

19. Point B is between points A and C. If

AC=32, AB = 17, and BC = 3m, draw a

diagram labeling the value for each

segment:

Equation to solve for m:

m = _______________

BC = ______________


AC=7b+13, AB = 25, and BC = 3b, draw a


segment:

Equation to solve for b:

b = _______________

AC = ______________

BC = ______________


AC=65, AB = 6c - 8, and BC = 3c+1,

draw a diagram labeling the value for each

segment:

Equation to solve for :c

c = _______________

AB = ______________

BC = ______________

22. Point S is between points R and T. If

RS =16, ST = 2x, and RT = 5x+10,

draw a diagram labeling the value for each

segment:

Equation to solve for x:

x = ____

ST = ______

RT = ______


RS=3y+1, ST=2y, and RT = 21, draw a


segment:

Equation to solve for y:

y = ____

RS = ______

ST = ______


RS =4y-1, ST = 2y-1, RT = 5y, draw a


segment:

Equation to solve for y:

y = ____

RS = ______

ST = ______

RT = ______

Use the figure to determine whether each pair of segments is congruent. Fill the space with the appropriate symbol ( , ), and if

appropriate draw tick marks on the diagram.

25. _____AB CD

26. _____XY YZ Hint: solve for x first

27. _____NP MP

Honors Geometry Page 19 & 20: 20, 26, 32, 39, 35 1.2 Textbook Homework







of tools and methods.

Student Learning Target

1. Students will be able to find the distance between two

points.

2. Students will find the midpoint of a segment.

Section 1.3 Notes: Distance and Midpoints


Distance

Distance Formula

(on Number Line)

Example 1: Use the number line to find QR.


Distance Formula

(in Coordinate Plane)

Example 2: Find the distance between E(–4, 1) and F(3, –1).


Midpoint

Midpoint Formula

(on Number Line)

Example 3:

a) Given: ,

Find the value of x.

b) Is Q the midpoint of


Midpoint Formula

(in Coordinate Plane)

Example 4: Find the coordinates of M, the midpoint of ,GH

for G(8, –6), and H(–14, 12).

Example 5: Find the coordinates of D if E(–6, 4) is the

midpoint of DF and F has coordinates (–5, –3).


Segment bisector

Honors Geometry Pages 31 – 34: Numbers 12, 31, 32, 44, 52, 66, 70 1.3 Textbook Homework







of tools and methods.

Student Learning Target

1. Students will be able to measure and classify angles.

2. Students will be able to identify and use congruent angles

and the bisector of an angle.

Section 1.4 Notes: Angle Measure


Ray

Named by:

Opposite Rays

Angle

Named By :

Sides

Vertex

Interior of the Angle

Exterior of the Angle

Example 1: Use the diagram below.

a) Name all angles that have B as a vertex.

b) Name the sides of 5.

c) Write another name for 6.

Classifying Angles


Right Angle

Symbol that indicates a 90 degree angle :

Acute Angle

Obtuse Angle

Congruent Angles

Symbol that indicates congruent angles:

Example 2:

a) Measure TYV and classify it as right, acute, or obtuse.

b) Measure WYT and classify it as right, acute, or obtuse.

c) Measure TYU and classify it as right, acute, or obtuse.

Example 3: and have the same measure.

If (

) and (

) is a straight angle?

Example 4: Given: is a straight angle. is a right angle.

( ( Solve for x and y.

A B D

C

T R S

X


Angle bisector

Example 5: Given: ( ( ( Has been trisected?

Example 6: RT bisects QRS. Example 7: KM bisects JKL.

Given that mQRS= 60 , what are The measures of the two congruent

the measures of QRT & TRS? angles are 2 7x b g and 4 41x b g .

Find the measures of JKM and

MKL.

Degrees, Minutes, and Seconds

Degree measure is divided into smaller portions, minutes and seconds. One degree is equivalent to minutes and one minute is

equivalent to 60 seconds.

1° = 60ʹ

1ʹ = 60ʹʹ

Example 7:

a) Convert5

1218

to degrees, minutes, and seconds. b) Convert

to degrees and minutes.

Example 8:

a) Change 7222’30’’ to degrees. b) Change 8450’ to degrees.

1

2 3

A B

C

Clock Problems

Example 9: Find the angle of the hands of the clock at:

a) 9:40 b) 3:50

c) 7:25 d) 11:20

Honors Geometry Clock Problems Worksheet 1. 8:20 2. 2:40

3. 1:45 4. 5:32

5. Convert3

465

into degrees, minutes and seconds.

6. Your latitude is 13°40ʹ20ʹʹ. In order to program these coordinates into your GPS, you must convert the measurement to degrees

only. [Hint: you are working backwards in the previous example.]

7. Two angles are complementary (they add to 90°). If one angle has a measure of 36°14ʹ25ʹʹ, find the measure of the second angle

(the complement).

8. The straight angle is divided by rays and RK RJ in the ratio of 6:4:2. Find the mJRT.

9. RQP is a right angle

mRQS = (2x + 19)°

mSQP = (7x – 10)°

Find the value of x.

Honors Geometry Pages 41 – 43: Numbers 28, 41, 44, 51 1.4 Textbook Homework

M R T

K

J

Q

P

S

R


G.SRT.7 Explain and use the relationship between the sine

and cosine of complementary angles.

Student Learning Targets

1. Students will be able to identify and use special pairs of

angles.

2. Students will be able to identify perpendicular lines.

Section 1.5 Notes: Angle Relationships

Vocabulary Definition Picture Non-examples

Adjacent Angles

Linear Pair

Vertical Angles

Special Characteristic -

Example 1:

a) Name an angle pair that satisfies the condition two angles

that form a linear pair.

b) Name an angle pair that satisfies the condition two right

vertical angles.

Angle Pair Relationships


Complementary Angles

Supplementary Angles

Example 2: Find the measures of two supplementary angles if

the measure of one angle is 6 less than five times the measure

of the other angle.

Example 3: Find the measures of two complementary angles

if the measures of the larger angle is 12 more than twice the

measure of the smaller angle.


Perpendicular Lines

Characteristics of Perpendicular Lines

1.

2.

3.

4.

Example 4: Find x and y so that KO and HM are perpendicular.

CAN be Assumed Diagram CANNOT be Assumed

Example 5: Determine whether the following statement can be justified from the figure below. Explain.

a) mVYT = 90°

b) TYW and TYU are supplementary.

c) VYW and TYS are adjacent angles.

Example 6: is a right angle. The ratio of the measures of and is 3 to 2.

Find . (Hint: Let and )

Honors Geometry Pages 51 & 52: Numbers 11, 24, 26, 28, 34, 36, 38, 39 1.5 Textbook Homework

C B

A

D


G.GPE.7 Use coordinates to compute perimeters of

polygons and areas of triangles and rectangles.

Student Learning Targets

1. Students will be able to identify and name polygons.

2. Students will be able to find the perimeter,

circumference, and area of two-dimensional figures.

Section 1.6 Notes: Two-Dimensional Figures


Polygon

Vertex of the Polygon

Examples of Polygons Examples of Not Polygons

Example 1: Determine if the following are polygons. If no, explain why.


Concave

Convex

N-gon

Number of Sides Polygon

3

4

5

6

7

8

9

10

11

12

N n-gon


Equilateral Polygon

Equiangular Polygon

Regular Polygon

Example 2: Name the polygon by its number of sides. Then classify it as convex or concave and regular or irregular. Provide a

justification in your decision.

a) b)

Justification: Justification:


Perimeter

Circumference

Area

Triangle Square Rectangle Circle

Perimeter: Perimeter: Perimeter: Perimeter:

Area:

Area:

Area:

Area:

Example 3:

a) Find the perimeter and area of the figure.

b) Find the circumference and area of the figure.

Example 4: Multiple Choice Terri has 19 feet of tape to mark an area in the classroom where the students may read. Which of these

shapes has a perimeter or circumference that would use most or all of the tape?

a) square with side length of 5 feet b) circle with the radius of 3 feet

c) right triangle with each leg length of 6 feet d) rectangle with a length of 8 feet and a width of 3 feet

Example 5: Find the perimeter and area of the figure on the right.

Example 6: You are putting a stone border along two sides of a rectangular Japanese garden

that measures 8 yards by 14 yards. Your budget limits you to only enough stone to

cover 104 square yards. How wide should the border be?

Perimeter and Area on the Coordinate Plane

Example 7: Find the perimeter and area of a pentagon

ABCDE with A(0, 4), B(4, 0), C(3, –4), D(–3, –4), and E(–3,

1).

Example 8: Find the perimeter of quadrilateral WXYZ with

W(2, 4), X(–3, 3), Y(–1, 0), and Z(3, –1).

8

14

Honors Geometry Pages 62 & 63: Numbers 26, 32, 45, 48 1.6 Textbook Homework

Here are the rules of the game. You are only allowed to use a straightedge (no measuring) and a

compass to construct the following. See if you can win the game. You’ve got this!!

Note: Visit http://www.mathopenref.com/tocs/constructionstoc.html for additional help.

1) Copy a Segment:

Practice YOU TRY

2) Bisect a Segment:

Practice YOU TRY

Chapter 1

http://www.mathopenref.com/tocs/constructionstoc.html

3) Copy an Angle:

4) Bisect an Angle:

Practice

YOU TRY

Practice

YOU TRY

5) Perpendiculars: a) Construct a line perpendicular to line l and passing through point P on l.

b) Construct a line perpendicular to line k and passing through point P not on k.

Practice

YOU TRY

Practice

YOU TRY

Reflective Questions: 1) How specifically does the compass help you? (Hint: Think about what it allows you to do without actually measuring

distance)

2) What do you think is the purpose of constructing something rather than measuring it out (this is open-ended; I want to

know what you think)?

3) Did you find this activity helpful in understanding vocabulary (i.e. bisector, perpendicular, etc.)? Explain. Be honest.

Practice (try without looking at the steps) 1)

2)

3)

4)

5a)

5b)

honors geometry chapter 1...

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