name date period lesson 1 reteach - school webmasters...lesson 2 extra practice complementary and...

Course 2 • Chapter 7 Geometric Figures 105

NAME _____________________________________________ DATE __________________ PERIOD _________

Copy

righ

t ©

The

McG

raw

-Hill

Com

pani

es, I

nc. P

erm

issi

on is

gra

nted

to

repr

oduc

e fo

r cl

assr

oom

use

.Lesson 1 ReteachClassify Angles

exactly 90°

Right Angle

less than 90°

Acute Angle

between 90° and 180°

Obtuse Angle

exactly 180°

Straight Angle

ExampleName each angle below. Then classify the angle as acute, right, obtuse, or straight.

1.

1

2.

2

Use the vertex as the middle letter Use the vertex or the number only,and a point from each side, ∠ABC, ∠D or ∠2. The angle is less than∠CBA, or use the vertex or the 90˚, so it is an acute angle.number only, ∠B or ∠1. The angle is 90˚, so it is a right angle.

3. What is the value of x in the figure at the right? The angle labeled 5x˚ and the angle labeled 55˚ are vertical angles. Since vertical angles are congruent, the value of x is 11.

ExercisesName each angle. Then classify the angle as acute, right, obtuse, or straight.

1.

3

2. 3.

4. Find the value of x in the figure at the right. (3x - 4)°

146°34°

• An angle is formed by two rays that share a common endpoint called the vertex.

• An angle can be named in several ways. The symbol for angle is ∠.

• Angles are classifi ed according to their measures. Two angles that have the same measure are said to be congruent.

• Two angles are vertical if they are opposite angles formed by the intersection of two lines. Vertical angles are congruent.

• Two angles are adjacent if they share a common vertex, a common side, and do not overlap.

5x°125°

55°

105_118_CC_A_RSPC2_C07_662331.indd 05 19/07/11 1:39 AM s-60user105_118_CC_A_RSPC2_C07_662331.indd Page 105 19/07/11 1:39 AM s-60userVolumes/110/GO00864/MIDDLE_SCHOOL_MATH/NATIONAL/ANCILLARY/ASSESSMENT_MASTERS_COURSE1-3..Volumes/110/GO00864/MIDDLE_SCHOOL_MATH/NATIONAL/ANCILLARY/ASSESSMENT_MASTERS_COURS

PDF Pass

Sherman Math 7 Weeks 1-3


NAME _____________________________________________ DATE __________________ PERIOD _________

Copy

righ

t ©

The

McG

raw

-Hill

Com

pani

es, I

nc. P

erm

issi

on is

gra

nted

to

repr

oduc

e fo

r cl

assr

oom

use

.Lesson 1 Homework PracticeClassify Angles

Use the figure at the right to answer Exercises 1–4.

1. Name two angles that are vertical.

2. Name two angles that are adjacent.

3. Find the value of x.

4. Find the value of y.

Name each angle in four ways. Then classify the angle as acute, right, obtuse, or straight.

5.

4

6.

2

7. 1

8.

3

9.

7

10.

6

Use the figure at the right to name the following.

11. two acute angles

12. two straight angles

13. two right angles

14. two obtuse angles

P

L

M

O

N

85°

95°

5x°5y°

105_118_CC_A_HWPSC2_C07_662334.indd Page 105 7/13/11 8:55 AM s-60user105_118_CC_A_HWPSC2_C07_662334.indd Page 105 7/13/11 8:55 AM s-60user /Volumes/110/GO00864/MIDDLE_SCHOOL_MATH/NATIONAL/ANCILLARY/.../Volumes/110/GO00864/MIDDLE_SCHOOL_MATH/NATIONAL/ANCILLARY/...

PDF Pass

NAME __________________________________________ DATE ____________ PERIOD _______

Lesson 1 Extra Practice

Classify Angles

Name each angle in four ways. Then classify each angle as acute, right, obtuse, or straight.

1.

2.

1, ABC, CBA, B; right 2, DEF, FED, E; obtuse

3.

3, LMN, NML, M; straight

4.

4, XYZ, ZYA, Y; acute

5.

5, KLM, MLK, L; acute

6.

6, RST, TSR, S; obtuse

Refer to the diagram at the right. Identify each angle pair as adjacent, vertical, or neither.

7. 1 and 2 adjacent 8. 2 and 5 neither 9. 1 and 3 vertical 10. 3 and 4 adjacent 11. 3 and 5 neither 12. 1 and 4 neither

Course 2 • Chapter 7 Geometric Figures


NAME _____________________________________________ DATE __________________ PERIOD _________

Copy

righ

t ©

The

McG

raw

-Hill

Com

pani

es, I

nc. P

erm

issi

on is

gra

nted

to

repr

oduc

e fo

r cl

assr

oom

use

.Lesson 2 ReteachComplementary and Supplementary Angles

• Two angles are complementary if the sum of their measures is 90°.

• Two angles are supplementary if the sum of their measures is 180°.

ExamplesIdentify each pair of angles as complementary, supplementary, or neither.

1. 150°30° 2.

16°74°

30° + 150° = 180° 16° + 74° = 90°

The angles are supplementary. The angles are complementary.

Example 3ALGEBRA Find the value of x.

Since the two angles form a straight line, they are supplementary. The sum of their measures is 180°.

35°5x°

5x + 35 = 180 Write the equation.

- 35 = -35 Subtract 35 from each side.

5x = 145 5 5 Divide each side by 5 x = 29 Simplify.

ExercisesIdentify each pair of angles as complementary, supplementary, or neither.

1.

43

2. 40°

50°

3.

120°70°

ALGEBRA Find the value of x in each figure.

4. 36° 6x°

5.

56°4x°

6. 22°

2x°

105_118_CC_A_RSPC2_C07_662331.indd Page 107 19/07/11 1:40 AM s-60user105_118_CC_A_RSPC2_C07_662331.indd Page 107 19/07/11 1:40 AM s-60userVolumes/110/GO00864/MIDDLE_SCHOOL_MATH/NATIONAL/ANCILLARY/ASSESSMENT_MASTERS_COURSE1-3..Volumes/110/GO00864/MIDDLE_SCHOOL_MATH/NATIONAL/ANCILLARY/ASSESSMENT_MASTERS_COURS

PDF Pass


NAME _____________________________________________ DATE __________________ PERIOD _________

Copy

righ

t ©

The

McG

raw

-Hill

Com

pani

es, I

nc. P

erm

issi

on is

gra

nted

to

repr

oduc

e fo

r cl

assr

oom

use

.Lesson 2 Homework PracticeComplementary and Supplementary Angles

Classify each pair of angles as complementary, supplementary, or neither.

1.

1 2

2.

12

3.

12


4.

22°

4x°

5.

65° (x + 2)°

6.

43°

(x - 7)°

7.

29°

(x - 5)°

8. 110°

7x°

9.

72° (x + 4)°

10.

49°

(x + 3)°

11.

92° 78°

x° 12.

19° (x - 50)°

13. ALGEBRA If ∠C and ∠D are supplementary, and the measure of ∠D is 45°, what is the measure of ∠C?

105_118_CC_A_HWPSC2_C07_662334.indd Page 107 7/13/11 8:55 AM s-60user105_118_CC_A_HWPSC2_C07_662334.indd Page 107 7/13/11 8:55 AM s-60user /Volumes/110/GO00864/MIDDLE_SCHOOL_MATH/NATIONAL/ANCILLARY/.../Volumes/110/GO00864/MIDDLE_SCHOOL_MATH/NATIONAL/ANCILLARY/...

PDF Pass

Course 2 • Chapter 7 Geometric Figures

NAME __________________________________________ DATE ____________ PERIOD _______

Lesson 2 Extra Practice

Complementary and Supplementary Angles

Identify each pair of angles as complementary, supplementary, or neither.

1.

2.

complementary supplementary

3.

4.

complementary neither

Find the measure of x in each figure.

5.

6.

70 20

7.

8.

40 20

KEY CONCEPTS: The Triangle Ineqaulity Theorem is a test to see if the triangle can exist or not. 1. Any one side of a triangle must be less than the sum of the other two sides. 3 Checks Equivalent "Greater than positive difference" check a < b + c b < a + c a > b - c c < a + b a > c - b 2. The result of any check of all 3 inequalities could be 0 ,1, 2 constraints or the triangle does not exist. 3. If any one inequality results in NOT TRUE then the triangle DOES NOT EXIST 4. If any one inequality results in ALWAYS TRUE then move on to check the other conditions as the given condition provides no constraints. 5. Any one side length must be greater than 0. i.e. x>-5 is not a constraint because x>0 is already more restrictive. 6. Students often learn to test if side a is less than b + c and then if a is greater than the positive difference of b and c rather than all 3 check, but in many cases the positive difference cannot be determined. e.g. a= 5 and b=2z and c=z + 5. Is 2z greater than z + 5?

* In order to be safe it is good to get in the habit of making all three checks unless the "positive" difference between the other sides is certain.

7. ** Like any equation and inequality plug your results back into the original conditions to make sure the numerical results make sense. TYPICAL MISTAKES TO WATCH FOR: 1. Be careful about the direction of the ineqaulity symbol. Many problems put the variable on the right side and force you to switch the entire inequality. e.g. 5 > y is not y > 5. It is y < 5 2. Do nto forget to change the direction of the inequality symbol if dividing by a negative! e.g. -y < -5 becomes y > 5 3. The inequality theorem conditions are "less than" only and NEVER include "equal than"

ua

ot

Program: CA EL Guides Component: SEPDF Proof

Vendor: Six Red Marbles Grade/Level: Course 2


NAME DATE PERIOD

Copy

right

© M

cGra

w-H

ill E

duca

tion.

Inquiry Lab Guided WritingCreate TrianglesWHAT do you notice about the measures of the sides or the measures of the angles that form triangles?

Use the exercises below to help answer the Inquiry question. Write the correct word or phrase on the lines provided.

1. Rewrite the question in your own words.

2. What key words do you see in the question?

3. Use the given triangles to fill in the table below. Find the sum of two side lengths of each triangle. Then write the length of the third side.

TriangleSum of sides

1 and 2Length of

side 3

A

B

C

The angle measures for three triangles are listed. Find each sum.

4. 60˚ + 30˚ + 90˚ =

5. 85˚ + 25˚ + 70˚ =

6. 55˚ + 75˚ + 50˚ =

WHAT do you notice about the measures of the sides or the measures of the angles that form triangles?

A

3 cm

3 cm

3 cm

B

5 cm

2 cm

4 cm

C

4 cm

1 cm

4 cm

075_085_EL_CA_SE_G7_C07_135686.indd 77 4/29/13 11:50 AM

Choose two sides of the triangle, add them together,and put the sum in "Sum of sides 1 and 2."Then write the length of the other (third) side in "Length of side 3."

Name: Date: WORKSHEET :

Triangle Inequality

Theorem

No, because 7+2 < 11 Yes, because 5+12 > 12

13-10 < x < 13+10 10 < x < 23

WORKSHEET :

Triangle Inequality

Theorem

Solve for x: Use Triangle Inequality theorem (a < b + c, b < a + c, c < a + b) to solve.


NAME _____________________________________________ DATE __________________ PERIOD _________

Copy

righ

t ©

The

McG

raw

-Hill

Com

pani

es, I

nc. P

erm

issi

on is

gra

nted

to

repr

oduc

e fo

r cl

assr

oom

use

.Lesson 1 ReteachClassify Angles

exactly 90°

Right Angle

less than 90°

Acute Angle

between 90° and 180°

Obtuse Angle

exactly 180°

Straight Angle

ExampleName each angle below. Then classify the angle as acute, right, obtuse, or straight.

1.

1

2.

2

Use the vertex as the middle letter Use the vertex or the number only,and a point from each side, ∠ABC, ∠D or ∠2. The angle is less than∠CBA, or use the vertex or the 90˚, so it is an acute angle.number only, ∠B or ∠1. The angle is 90˚, so it is a right angle.

3. What is the value of x in the figure at the right? The angle labeled 5x˚ and the angle labeled 55˚ are vertical angles. Since vertical angles are congruent, the value of x is 11.

ExercisesName each angle. Then classify the angle as acute, right, obtuse, or straight.

1.

3

2. 3.

4. Find the value of x in the figure at the right. (3x - 4)°

146°34°

• An angle is formed by two rays that share a common endpoint called the vertex.

• An angle can be named in several ways. The symbol for angle is ∠.

• Angles are classifi ed according to their measures. Two angles that have the same measure are said to be congruent.

• Two angles are vertical if they are opposite angles formed by the intersection of two lines. Vertical angles are congruent.

• Two angles are adjacent if they share a common vertex, a common side, and do not overlap.

5x°125°

55°

∠H or ∠3; acute

50

∠MNO, ∠ONM, or ∠N; obtuse

∠Q; right


PDF Pass


NAME _____________________________________________ DATE __________________ PERIOD _________

Copy

righ

t ©

The

McG

raw

-Hill

Com

pani

es, I

nc. P

erm

issi

on is

gra

nted

to

repr

oduc

e fo

r cl

assr

oom

use

.Lesson 2 ReteachComplementary and Supplementary Angles

• Two angles are complementary if the sum of their measures is 90°.

• Two angles are supplementary if the sum of their measures is 180°.

ExamplesIdentify each pair of angles as complementary, supplementary, or neither.

1. 150°30° 2.

16°74°

30° + 150° = 180° 16° + 74° = 90°

The angles are supplementary. The angles are complementary.

Example 3ALGEBRA Find the value of x.

Since the two angles form a straight line, they are supplementary. The sum of their measures is 180°.

35°5x°

5x + 35 = 180 Write the equation.

- 35 = -35 Subtract 35 from each side.

5x = 145 5 5 Divide each side by 5 x = 29 Simplify.

ExercisesIdentify each pair of angles as complementary, supplementary, or neither.

1.

43

2. 40°

50°

3.

120°70°


4. 36° 6x°

5.

56°4x°

6. 22°

2x°

supplementary

6

complementary

31

neither

34


PDF Pass

ANSWERS :

Triangle Inequality

Theorem

Solve for x: Use Triangle Inequality theorem (a < b + c, b < a + c, c < a + b) to solve.

10 < 3x + x - 2 12 < 4x 3 < x 3x < 10 + x - 2 2x < 8 x < 4 x - 2 < 10 + 3x -12 < 2x 6 < -6 3 < x < 4

2x < 3x + x 2x < 4x 2 < 4 ALWAYS TRUE 3x < 2x + x 3x < 3x 3 < 3 NOT TRUE x < 2x + 3x x < 5x 1 < 5 ALWAYS TRUE Triangle cannot exist

5 < x - 1 + x + 2 5 < 2x + 1 x > 2 x - 1 < 5 + x + 2 -1 < 7 ALWAYS TRUE x + 2 < 5 + x - 1 2 < 4 ALWAYS TRUE x > 2

5 < x + 8 -3 < x x > 0 already true 8 < 5 + x x > 3 x < 5 + 8 x < 13 3 < x < 13

5 < 2x + x + 2 3 < 3x 1 < x 2x < 5 + x + 2 x < 7 x + 2 < 5 + 2x -3 < x x > 0 already true 1 < x < 7

4 < 5 - x + 2x -1 < x x > 0 already true 2x < 4 + 5 - x x < 9 5 - x < 4 + 2x 1 < x 1 < x < 9

name date period lesson 1 reteach - school webmasters...lesson 2 extra practice complementary and...

Documents