Geometry: CC 2019>Chapter 3>Section 3.1>Exercises 1 - 31

Covid Week 4 (Ch 3 Review)

Geometry: CC 2019>Chapter 3>Section 3.1>Exercises 1 - 31> Question #3

1. Think of each segment in the diagram as part of a line. All the angles are right angles. Which line(s)

contain(s) point and appear to be parallel to ?B CD←→

AB←→

AE←→

BC←→

BF←→

Geometry - DecosterPlease take a few pictures and email them to me once completed. [email protected]



contain(s) point and appear to be perpendicular to ?B CD←→

AB←→

AE←→

BC←→

BF←→




contain(s) point and appear to be skew to ?

B CD←→

AB←→

AE←→

BC←→

BF←→

4. Use the diagram to name a pair of parallel lines.

and MK←→−

LS←→

and PR←→

MK←→−

and NP←→

PQ←→

and PR←→

PQ←→



5. Use the diagram to name a pair of perpendicular lines.

and MK←→−

LS←→

and PR←→

MK←→−

and NP←→

PQ←→

and PR←→

PQ←→

6. Identify all pairs of corresponding angles.

and ∠1 ∠5 and ∠2 ∠7 and ∠4 ∠5

and ∠1 ∠8 and ∠3 ∠6 and ∠4 ∠6

and ∠2 ∠6 and ∠3 ∠7 and ∠4 ∠8



7. Identify all pairs of alternate interior angles.

and ∠1 ∠5 and ∠3 ∠5 and ∠4 ∠5

and ∠1 ∠8 and ∠3 ∠6 and ∠4 ∠6

and ∠2 ∠6 and ∠3 ∠7 and ∠4 ∠8

8. Identify all pairs of alternate exterior angles.

and ∠1 ∠7 and ∠2 ∠7 and ∠4 ∠5

and ∠1 ∠8 and ∠3 ∠6 and ∠4 ∠6

and ∠2 ∠6 and ∠3 ∠7 and ∠4 ∠8



9. Identify all pairs of consecutive interior angles.

and ∠1 ∠5 and ∠3 ∠5 and ∠4 ∠5

and ∠2 ∠6 and ∠3 ∠6 and ∠4 ∠6

and ∠2 ∠7 and ∠3 ∠7 and ∠4 ∠8

10.

Use the diagram to find the measures of all the angles, given that .m∠1 = 76°

m∠2 = °

m∠3 = °

m∠4 = °


11.

Use the diagram to find the measures of all the angles, given that .m∠2 = 159°

m∠1 = °

m∠3 = °

m∠4 = °

12.

by the

.

by the

.

Find and . Tell which theorem can be used.m∠1 m∠2

m∠1 =

m∠2 =

63° 117° Alternate Exterior Angles Theorem

Consecutive Interior Angles Theorem Alternate Interior Angles Theorem

Vertical Angles Congruence Theorem



13.

by the

.

by the

.

Find and . Tell which theorem can be used.m∠1 m∠2

m∠1 =

m∠2 =

40° 140° Corresponding Angles Theorem

Alternate Exterior Angles Theorem Consecutive Interior Angles Theorem

Alternate Interior Angles Theorem Vertical Angles Congruence Theorem



14.

Complete the steps to find the value of . x

2x =

x =

15.

Complete the steps to find the value of . x

+ (7x + 24) = 180

7x+ = 180

7x =

x =


16.

DRAWING CONCLUSIONS You are designing a box like the one shown.

The measure of is . Find and .∠1 70° m∠2 m∠3

m∠2 = °

m∠3 = °

In the closed box, and form a linear pair, so . These angles do not change in

the open box, so , and is a straight angle.

Explain why is a straight angle.∠ABC

∠2 ∠ m∠2 + m∠ = °

m∠2 + m∠ = ° ∠ABC

If is , will still be a straight angle? Will the opening of the box be more steep or less steep?Explain.

m∠1 60° ∠ABC

will still be a straight angle; will be and will be . Theopening of the box will be less steepbecause is smaller.

∠ABC m∠1

60° m∠3 120°

m∠1

will still be a straight angle; will be and will be . Theopening of the box will be more steepbecause is smaller.

∠ABC m∠1

60° m∠3 120°

∠1

will no longer be a straight angle; will be and will be ,

but will be . The opening of thebox will have a part that has the samesteepness and a part that is less steep.

∠ABC

m∠1 60° m∠3 120°

m∠2 70°

will no longer be a straight angle; will be and will be ,

but will be . The opening of thebox will have a part that has the samesteepness and a part that is more steep.

∠ABC

m∠1 60° m∠3 120°

m∠2 70°



17.

Find the value of that makes . x m ∥ n

x =

18.


x =

19.


x =





20.


x =

21.

You prove .

Decide whether there is enough information to prove . If so, state the theorem you would use.m ∥ n

m ∥ n

22.

You prove .

Decide whether there is enough information to prove . If so, state the theorem you would use. m ∥ n

m ∥ n



23.

You prove .

Decide whether there is enough information to prove . If so, state the theorem you would use. m ∥ n

m ∥ n

24.Are and parallel? Explain your reasoning.AC

←→DF←→

yes; By the Vertical Angles Congruence Theorem, . So, and are parallelbecause vertical angles are congruent.

m∠FEB = 123° AC←→

DF←→

yes; By the Linear Pair Postulate, . So, and are parallel by theCorresponding Angles Converse.

m∠DEB = 57° AC←→

DF←→

no; Because the consecutive exterior angles are not congruent, and are not parallel.AC←→

DF←→

no; Because the alternate exterior angles are not supplementary, and are not parallel.

AC←→

DF←→


25.Are and parallel? Explain your reasoning.AC

←→DF←→

yes; By the Linear Pair Postulate, . So, and are parallel by theCorresponding Angles Converse.

m∠BEF = 143° AC←→

DF←→

yes; By the Linear Pair Postulate, . So, and are parallel because verticalangles are congruent.

m∠ABE = 143° AC←→

DF←→

no; Because the alternate exterior angles are not congruent, and cannot be parallel.AC←→

DF←→

no; Because the alternate interior angles are not congruent, and cannot be parallel.AC←→

DF←→




26.

The angle marked and are corresponding angles of parallel lines, so .

and are alternate interior angles.

So, by the Alternate Interior Angles Converse, the top of the step will be parallel to the floor when

.

MODELING WITH MATHEMATICS One way to build stairs is to attach triangular blocks to an angledsupport, as shown. The sides of the angled support are parallel. If the support makes a angle with thefloor, explain what must be so the top of the step will be parallel to the floor.

32°m∠1

32° ∠ m∠2 = °

∠2 ∠

m∠1 =

°

27.

The distance between the points is about units

Use the Distance Formula to find the distance between and , rounded to the nearesthundredth.

(1, 3) (−2, 9)

28.

The distance between the points is about units.

Use the Distance Formula to find the distance between and , rounded to the nearesthundredth.

(−3, 7) (8, − 6)






29. Simplify the ratio.

= 6 − (−4)

8 − 3

30. Simplify the ratio.

= 3 − 5

4 − 1

31.

The slope of the line is , the -intercept is .

Identify the slope and the -intercept of the line.y

y = 3x + 9

y

32.

The slope of the line is , the -intercept is .

Identify the slope and the -intercept of the line.y

y = − x + 712

y

33.

The slope of line 1 is .


Tell whether the lines through the given points are parallel, perpendicular, or neither.

Line 1:

Line 2:

(1, 0) , (7, 4)

(7, 0) , (3, 6)

The two lines are .



34.




Line 1:

Line 2:

(−3, 1) , (−7, −2)

(2, −1) , (8, 4)

The two lines are .

35.




Line 1:

Line 2:

(−9, 3) , (−5, 7)

(−11, 6) , (−7, 2)

The two lines are .


36. Write an equation of the line passing through point that is parallel to the line .

P (0, − 1) y = − 2x + 3

y =

Graph the equations of the lines to check that they are parallel.

Line Undo Redo Reset

1 2 3 4 5−1−2−3−4−5

1

2

3

4

5

−1

−2

−3

−4

−5

0


37. Write an equation of the line passing through point that is parallel to the line .

P (3, 8) y = (x + 4)15

y =

Graph the equations of the lines to check that they are parallel.


1 2 3 4 5 6 7−1−2−3−4

1

2

3

4

5

6

7

8

9

−1

0


38. Write an equation of the line passing through point that is perpendicular to the line

.P (0, 0)

y = − 9x − 1

y =

Graph the equations of the lines to check that they are perpendicular.


1 2 3 4 5 6 7 8 9 10−1−2

1

2

3

4

5

6

7

8

9

10

−1

−2

0


39.

Write an equation of the line passing through point that is perpendicular to the line .P (4, −6) y = −3

x =

Graph the equations of the lines to check that they are perpendicular.


2 4 6 8 10−2−4−6−8−10

2

4

6

8

10

−2

−4

−6

−8

−10

0



40. ERROR ANALYSIS Describe the error in writing an equation of the line that passes through the point and is parallel to the line .(3, 4) y = 2x + 1

The - and -coordinates are substituted for the wrong variables.x y

The -intercept should be solved for instead of the slope .y b m

To find , standard form must be used instead of slope-intercept form.m

Once the new slope is found, the new -intercept must also be found.y

The line is parallel to the line and passes through the point .

Correct the error.

y = y = 2x + 1 (3, 4)

41.

The midpoint is , .

The equation of the perpendicular bisector is .

Find the midpoint of with endpoints and . Then write an equation of the line that

passes through the midpoint and is perpendicular to . This line is called the perpendicular bisector.

PQ¯ ¯¯̄¯̄ ¯̄

P (−4, 3) Q (4, −1)

PQ¯ ¯¯̄¯̄ ¯̄

( )

y =

Documents

Geometry: CC 2019>Chapter 3>Section 3.1>Exercises 1 - 31