introduction to geometry and geometric constructions assignments...introduction to geometry and...

Chapter 9 Assignments • 181

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Lesson 9.1 Assignment

Name ________________________________________________________ Date _________________________

Earth MeasureIntroduction to Geometry and Geometric Constructions

Use a compass and a straightedge to complete Questions 1 and 2.

1. Construct a flower with 12 petals by following these steps.

a. Open your compass to an appropriate radius length. (You will not change the radius of the

compass for this entire construction.)

b. Construct a circle in the space provided.

c. Place the point of your compass on the circle and draw an arc that goes from one side of the

circle to the other.

d. Place the point of your compass at a point where the arc intersects the circle and draw another

arc from one side of the circle to the other.

182 • Chapter 9 Assignments

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Lesson 9.1 Assignment page 2

e. Repeat step (d) until you have a flower with 6 petals.

f. Place the point of your compass on the circle between 2 petals and draw an arc that goes from

one side of the circle to the other.

g. Place the point of your compass on the circle where the arc intersects the circle and draw an

arc from one side of the circle to the other.

h. Repeat step (g) until you have a flower with a total of 12 petals.

i. Color your flower.


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2. Construct a honeycomb by following these steps.

a. Open your compass to an appropriate radius length. (You will not change the radius of the

compass for this entire construction.)

b. Construct a circle in the space provided. Place the point of your compass on the circle and

construct another circle.

c. Place the point of your compass on the intersection of the two circles and construct another

circle. Repeat this step until you have six petals.

d. Use your straight edge to connect the tips of the petals with line segments to form a hexagon.


Name ________________________________________________________ Date _________________________


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e. Construct another six petals by placing the point of your compass on the intersection of two

of the outer circles and drawing another circle. Then, use arcs to complete the construction of

another six petals in the new circle. Use your straight edge to connect the tips of the petals to

form another hexagon.

f. Repeat step (e) all around the original hexagon until you have a honeycomb with 7 hexagons.

g. Color and decorate your honeycomb.


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Name ________________________________________________________ Date _________________________

Angles and More AnglesMeasuring and Constructing Angles

1. Use a straightedge and a compass to complete parts (a) through (k).

a. Draw an acute angle.

Answers will vary.

S

R

T

b. Name and label the angle you drew in part (a) angle RST.

See figure in part (a).

c. What rays form RST?

___ › SR and

___ › ST

d. What is the measure of RST?

The measure of /RST is 50°.

e. Duplicate RST. Name and label the new angle XYZ.

Y

X

Z


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f. What rays form XYZ?

___ › YX and

___ › YZ

g. Is RST congruent to XYZ? Use your protractor to justify your answer.

Yes. /RST is congruent to /XYZ because both angles have a measure of 50°.

h. Construct an angle that is twice the measure of RST.

E

D

F

i. Name and label the angle you drew in part (h) angle DEF.

See figure in part (h).

j. Complete the following statement.

The measure of DEF is 100° .

k. Explain how you determined the measure of DEF.

I used a protractor to measure the angle.

OR

Because the measure of /DEF is twice the measure of /RST, I know that the measure of

/DEF is 2 3 50° or 100°.


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Name ________________________________________________________ Date _________________________

2. Use a straightedge and a compass to complete parts (a) through (h).

a. Draw an obtuse angle.

Answers will vary.

M

K L

J

b. Name and label the angle you drew in part (a) angle JKL.


c. What rays form JKL?

___ › KJ and

___ › KL

d. What is the measure of JKL?

The measure of /JKL is 130°.

e. Construct the bisector of JKL.


f. Name and label the angle bisector

___ › KM.


g. What is the measure of MKL? Explain how you found your answer.

The measure of /MKL is 65°.

I found my answer by using my protractor.

OR

The measure of /JKL is 130°. Because

____ › KM is the bisector of the angle,

I know that the measure of /MKL is 130° 4 2 or 65°.


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h. Is JKM congruent to MKL? Explain your reasoning.

Yes. /JKM is congruent to /MKL because these two angles were formed by bisecting a

larger angle. By definition, a bisector divides an angle into two equal parts.

3. Complete parts (a) through (d) to construct a 30° angle four different ways.

a. Draw a 30° angle using only a protractor and straightedge.

b. Use H to construct a 30° angle. Label the 30° angle GHI. (HINT: Measure the angle to help

you decide how to use it to construct a 30° angle.)

I

G

H

c. Use P to construct a 30° angle. Label the 30° angle OPQ.

Q

O

P

d. Use Q to construct a 30° angle. Label the 30° angle PQR.

R

P

Q


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Special AnglesComplements, Supplements, Midpoints, Perpendiculars, and Perpendicular Bisectors

1. Draw the supplementary angles described and answer the questions in parts (a) through (e).

a. Draw a pair of supplementary adjacent angles. One of the angles should have a measure of

85°. Label each angle with its measure.

95° 85°

b. Draw a pair of supplementary angles that are NOT adjacent but share a common vertex. One of

the angles should have a measure of 85°. Label each angle with its measure.

85°95°


Name ________________________________________________________ Date _________________________


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c. Draw a pair of supplementary angles that are NOT adjacent and do NOT share a common

vertex. One of the angles should have a measure of 85°. Label each angle with its measure.

85°95°

d. What do the pairs of angles in parts (a) through (c) have in common?

In each pair, one of the angles has a measure of 85° and the other one has a measure of 95°.

The sum of the measures of each pair is 180°.

e. What is the difference between the pairs of angles in parts (a) through (c)?

The pairs of angles are not always adjacent and do not always share a vertex.

2. Draw the complementary angles described and answer the questions in parts (a) through (e).

a. Draw a pair of complementary adjacent angles. One of the angles should have a measure of

62°. Label each angle with its measure.

62°

28°


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Name ________________________________________________________ Date _________________________

b. Draw a pair of complementary angles that are NOT adjacent but share a common vertex. One

of the angles should have a measure of 62°. Label each angle with its measure.

62°

28°

c. Draw a pair of complementary angles that are NOT adjacent and do NOT share a common

vertex. One of the angles should have a measure of 62°. Label each angle with its measure.

28° 62°

d. What do the pairs of angles in parts (a) through (c) have in common?

In each pair, one of the angles has a measure of 62° and the other angle has a measure of

28°. The sum of the measures of each pair is 90°.

e. What is the difference between the pairs of angles in parts (a) through (c)?

The pairs of angles are not always adjacent and do not always share a vertex.

3. Draw the angle pairs described and answer the questions in parts (a) through (c).

a. Draw a linear pair of angles. One of the angles should have a measure of 123°. Label each

angle with its measure.

123°57°


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b. Draw two angles with the same measures as those in part (a), such that they are NOT

a linear pair.

Sample answer.

123°

57°

c. Explain the differences and similarities between linear pairs and supplementary angles.

The sum of the measures of a linear pair of angles is 180°. The sum of the measures of

supplementary angles is also 180°. Linear pairs are always supplementary. However,

supplementary angles are not always linear pairs because they do not have to be

adjacent or share a vertex.

4. Draw two intersecting lines that are not perpendicular to each other. Use these lines to complete

parts (a) through (f).

Answers will vary.

12

34

a. Label the angles 1, 2, 3, and 4.

See figure.

b. Name the vertical angles.

/1 and /3

/2 and /4


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Name ________________________________________________________ Date _________________________

c. Name all linear pairs.

/1 and /2

/2 and /3

/3 and /4

/4 and /1

d. Name all supplementary angles.

/1 and /2

/2 and /3

/3 and /4

/4 and /1

e. Name all pairs of adjacent angles.

/1 and /2

/2 and /3

/3 and /4

/4 and /1

f. Did you need to measure any of the angles to complete parts (b) through

(e)? Explain your reasoning.

No. I did not need to measure the angles. I know that vertical angles are two nonadjacent

angles that are formed by two intersecting lines and that they are congruent. I know that two

adjacent angles that form a straight line are linear pairs, and therefore they are supplementary.

I also know that adjacent angles are angles that share a common vertex and a common side.


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5. Use the figure shown to complete parts (a) through (h).

R A

S Q

a. Construct a perpendicular through point S.

See figure.

b. Use your compass to measure the distance between S and Q. Mark that distance off on the

perpendicular you constructed in part (a).

See figure.

c. Label the new point R.

See figure.

d. Construct a perpendicular through point R.

See figure.

e. Use your compass to measure the distance between S and Q. Mark that distance off on the

perpendicular you constructed in part (d).

See figure.

f. Label the new point A.

See figure.

g. Use your straightedge to draw a segment to connect points A and Q.

See figure.

h. What is the name of the figure you constructed? How do you know?

The figure has four congruent sides and four congruent angles, so it is a square.

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