GEOMETRY - White Plains Public Schools / Overvie · Chapter 1 – 2 Warm – Up Notes: ... Example...

GEOMETRY

Chapter 1: Foundations for Geometry

Name:______________________________ Teacher:____________________________ Pd: _______

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Table of Contents

Lesson 1.1: SWBAT: Identify, name, and draw points, lines, segments, rays, and planes.

Pgs: 1-4

Lesson 1.2: SWBAT: Use the length and midpoint of a segment to calculate the missing

lengths. Pgs: 5-10

Lesson 1.3: SWBAT: Name, classify and calculate the measure of angles.

Pgs: 11-14

Full Period Quiz Lessons: 1.1-1.3

Lesson 1.4: SWBAT identify adjacent, vertical, complementary, supplementary and calculate

the measures of pairs of angles.

Pgs: 15-19

Lesson 1.6: SWBAT: apply the formulas for midpoint and distance in conjunction with the

Pythagorean Theorem to find the length of a line segment.

Pgs: 20-23

Full Period Quiz Lessons: 1.4 and 1.6

Practice Test:

Pgs: 24-25

SWBAT: Identify, name, and draw points, lines, segments, rays, and planes.

1

Chapter 1 – 1

Warm – Up: Complete the chart in pencil.

Terms Labels Diagrams

Plane

Point

Line

A lowercase letter or two

points on the line.

line l

A capital letter point P

A script capital letter or 3

points not on a line.

plane R or plane ABC

Term Definition Label/Name Diagram

______, names a location

and has no size. It is

represented by a dot.

______, is a straight path

that has no thickness and

extends forever.

______, is a flat surface

that has no thickness and

extends forever.

Points that lie on the same line are collinear. K, L, and M are collinear.

K, L, and N are noncollinear.

Points that lie on the same plane are coplanar. Otherwise they are noncoplanar.


2

Example 1: Naming Points, Lines, and Planes

A. Name four coplanar points.

B. Name three lines.

Directions: Complete the chart below in pencil.

Terms Labels Diagrams

Ray

Endpoint

Opposite Rays

Segment

A capital letter,

C and D

It’s endpoint and any other

point on the ray

The common endpoint and any

other point on each ray

The two endpoints

Term Definition Labels/Name Diagram

is the part of a line

consisting of two points,

and all points between

them.

is a point at one end of a

segment or the starting

point of a ray

is a part of a line that

starts at an endpoint and

extends forever in one

direction

are two rays that have a

common endpoint and

form a line.


3

Example 2: Draw and label each of the following.

A. a segment with endpoints M and N. B. opposite rays with a common endpoint T.

A postulate, or axiom, is a statement that is accepted as true without proof. Postulates about points, lines, and

planes help describe geometric properties.

Example 3: Name a plane that contains three noncollinear points.

Use a dashed line to show the hidden parts of any figure that you are drawing. A dashed line will indicate the

part of the figure that is not seen.

Example 4: Sketch a figure that shows each of the following.

A. Two lines intersecting in exactly one point.

B. Two planes intersecting in one line.


4

Homework: pg 9 Numbers 1-21

Homework: Page 9, #'s 1 - 21

SWBAT: Use the length and midpoint of a segment to calculate the missing lengths.

5

Chapter 1 – 2

Warm – Up

Notes:


6

Example 1: Finding the Length of a Segment

Find each length.

Practice: Finding the Length of a Segment

Find each length.

In order for you to say that a point B is between two points A and C, all three points must lie on the same line,

and AB + BC = AC.


7

Example 2: Using the Segment Addition Postulate

M is between N and O. Find NO.

Practice: Using the Segment Addition Postulate

E is between D and F. Find DF.

The midpoint M of AB is the point that

bisects, or divides, the segment into two

congruent segments. If M is the midpoint of AB, then AM = MB.

So if AB = 6, then AM = 3 and MB = 3.


8

Example 3: Using Midpoints to Find Lengths

Practice:

Challenge:


9


10

Homework: Page 17, #'s 3, 4, 6, 7, 9, 10, 15, 17, 18

SWBAT: Name, classify and calculate the measure of angles.

11

Chapter 1 – 3

Warm – Up

Example 1: Naming Angles

An is a figure formed by two rays, or sides, with a common endpoint called the (plural:

vertices). You can name an angle several ways: by its vertex, by a point on each ray and the vertex, or by a

number.

Practice: Naming Angles

1. A surveyor recorded the angles formed by a transit (point A) and three distant points, B, C, and D.

Name three of the angles.

2. Write the different ways you can name the angles in the diagram.

U is the midpoint of TV, TU = 3x + 4,and UV = 5x - 2. Find TU, UV, and TV.


12

Directions: Match the terms with its correct image in pencil.

Congruent angles are angles that have the same measure. In the diagram, m ABC = m DEF, so you can write ABC DEF. This is read as “angle ABC

is congruent to angle DEF.” Arc marks are used to show that the two angles are congruent.


13

Example 2: Using the Angle Addition Postulate

Practice: Using the Angle Addition Postulate

Example 3: Finding the Measure of an Angle

KM bisects JKL, m JKM = (4x + 6)°, and m MKL = (7x – 12)°. Find m JKM.

Practice: Find the measure of each angle.


14

Homework

Holt: pages 24- 27 #'s 9-10, 17-18, 29-31,& 41 - 43

QS bisects PQR, m PQS = (5y – 1)°, andm PQR = (8y + 12)°. Find m PQS.

SWBAT identify adjacent, vertical, complementary, supplementary and calculate the measures of pairs of angles.

15

Warm Up:

Pairs of Angles

Adjacent angles:

Linear pair:

a)

b)

a)

b)

Use the diagram below for questions 1 and 2.

1. Identify angles those are only adjacent.

2. Identify angles that are not adjacent.


16

Use the diagram below for question 3.

3. Identify angles that are adjacent and form a linear pair.

Complementary angles:

Supplementary angles:


17

Practice Problems

Ex. 4: Finding the measures of complements and supplements

a) complement of F b) complement of E

c) supplement of F d) supplement of G

Ex 5. An angle is 10 more than 3 times the measure of its complement. Find the measure of the complement.

Ex 6. An angle’s measure is 12 more than ½ the measure of its supplement. Find the measure of the angle.

Ex 7. Write an equation to find the measure of angle x.


18

8) If the m ABC = (4x – 10)o, and m CBD = (2x + 40)

o then what is x, m ABC and m CBD?

Vertical angles:__________________________________________________________

Ex 9: In the accompanying diagram, line a intersects line b.

What is the value of x?

Ex10: AB and CD intersect at E. If 205 xAECm and ,50 xBEDm

find, in degrees, .CEBm

A

B

C

D

x = _____ o

m ABC = _____ o

m CBD = _____ o


19

Homework: For homework help go to: http://my.hrw.com, username: square2, password: e7p4v and select

pg 32. Do #’s 14-22, 24, and 26-31.

http://my.hrw.com/

SWBAT: apply the formulas for midpoint and distance in conjunction with the Pythagorean Theorem to find the length of a line segment.

20

Chapter 1 – 6 Warm – Up

1. Find CD.

2.

3. Find the missing side length.

Example 1:

a.

b.


21

Practice:

a.

b.

c.

Example 2: Finding the Coordinates of an endpoint when given a midpoint.

Practice: Finding the Coordinates of an endpoint when given a midpoint.

a.

b.


22

Example 3:

a.

b.

Practice:

a.

b.

c.

d.


23

Homework

Name__________________________ Geometry – Chapter 1

Date___________________________ Practice Test

WORKSPACE

15. In the accompanying figure, two lines

intersect, intersect, m<1 = (4x – 20)°, and

m<3 = (2x – 40)°. Find the number of

degress in m<2.

GEOMETRY - White Plains Public Schools / Overvie · Chapter 1 – 2 Warm – Up Notes: ... Example...

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