Introduction to Geometry: Points, Lines, and Planes

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# Introduction to Geometry: Points, Lines, and Planes - PowerPoint PPT Presentation

Use the figure to name each of the following. Name a point with a capital letter. H, I, J, and K. HO. Name a segment by its endpoints. , HJ. , KI. , and OI. c. five other names for KI. , OK. , and. OI. There is one line pictured. It has several names. IK. , KO. , IO.

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Use the figure to name each of the following.

Name a point with a capital letter.

H, I, J, and K

HO

Name a segment by its endpoints.

, HJ

, KI

, and OI

c. five other names for KI

, OK

, and

OI

There is one line pictured. It has several names.

IK

, KO

, IO

d. five different rays

HO

The first letter names the endpoint of the ray.

, OJ

, KI

, OK

, and JH

Introduction to Geometry: Points, Lines, and Planes

Lesson 9-1

a. four points

b. four different segments

MP, OP, QT, ST

MQ, NR, OS

MN, NO, QR, RS

Introduction to Geometry: Points, Lines, and Planes

Lesson 9-1

You are looking directly down into a wooden crate. Name each of the following.

a. four segments that intersectPT

b. three segments parallel to PT

c. four segments skew to PT

First draw two lines that intersect.

Then draw a segment that is parallel to one of the lines.

Introduction to Geometry: Points, Lines, and Planes

Lesson 9-1

Draw two intersecting lines. Then draw a segment that is parallel to one of the intersecting lines.

Use the lines on notebook or graph paper.

m 3 + m 4 = 180°

3 and 4 are supplementary.

m 3 + 110° = 180°

Replace m 4 with 110°.

m 3 + 110° – 110° = 180° – 110°

Solve for m 3.

m 3 = 70°

Angle Relationships and Parallel Lines

Lesson 9-2

Find the measure of 3 if m 4 = 110°.

1 3, 2 4, 5 7, 6 8

2 7, 6 3

Angle Relationships and Parallel Lines

Lesson 9-2

In the diagram, p || q. Identify each of the following.

a. congruent corresponding angles

b. congruent alternate interior angles

Classifying Polygons

Lesson 9-3

Classify the triangle by its sides and angles.

The triangle has no congruent sides and one obtuse angle.

The triangle is a scalene obtuse triangle.

Classifying Polygons

Lesson 9-3

Name the types of quadrilaterals that have at least

one pair of parallel sides.

All parallelograms and trapezoids have at least one pair of parallel sides.

Parallelograms include rectangles, rhombuses, and squares.

Classifying Polygons

Lesson 9-3

A contractor is framing the wooden deck shown below in the shape of a regular dodecagon (12 sides). Write a formula to find the perimeter of the deck. Evaluate the formula for a side length of 3 ft.

To write a formula, let x = the length of each side.

The perimeter of the regular dodecagon is

x + x + x + x + x + x + x + x + x + x + x + x.

Therefore a formula for the perimeter is P = 12x.

P = 12xWrite the formula.

= 12(3)   Substitute 3 for x.

= 36 Simplify.

For a side length of 3 ft, the perimeter is 36 ft.

One strategy for solving this problem is to draw a diagram and count the diagonals. A nonagon has nine sides.

You can draw six diagonals from one vertex of a nonagon.

AH, AG, AF, AE, AD, and AC are some of the diagonals.

Problem Solving Strategy: Draw a Diagram

Lesson 9-4

How many diagonals does a nonagon have?

Problem Solving Strategy: Draw a Diagram

Lesson 9-4

(continued)

You can organize your results as you

count the diagonals. Do not count a

diagonal twice. (The diagonal from A to

C is the same as the one from C to A.)

Then find the sum of the numbers

of diagonals.

Vertex

Number of Diagonals

6

A

6

B

5

C

4

D

E

3

F

2

G

1

H

0

I

0

Total

27

A nonagon has 27 diagonals.

X

, T

W

, TUV

WUX

V

WX

, TU

WU

, VU

XU

TV

c. Find the length of WX.

WX,

TV,

and

TV = 300 m, WX = 300 m.

Since

Congruence

Lesson 9-5

In the figure, TUV WUX.

a. Name the corresponding congruent angles.

b. Name the corresponding congruent sides.

ACB

ECD

Angle

AC

EC

Side

CAB

CED

Angle

by ASA.

ACB

ECD

Congruence

Lesson 9-5

List the congruent corresponding parts of each pair of triangles. Write a congruence statement for the triangles.

a.

MK

LJ

Side

MKJ

LJK

Angle

JK

JK

Side

MKJ

LJK

by SAS.

Congruence

Lesson 9-5