Download geometry - White Plains Public Schools

GEOMETRY
Chapter 1: Foundations for Geometry
Name:______________________________
Teacher:____________________________
Pd: _______
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.
Chapter 1 – 1
Warm – Up: Complete the chart in pencil.
Terms
Plane
Labels
A lowercase letter or two
points on the line.
Diagrams
Point
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.
1
SWBAT: Identify, name, and draw points, lines, segments, rays, and planes.
Example 1: Naming Points, Lines, and Planes
A. Name four coplanar points.
B. Name three lines.
Directions: Complete the chart below in pencil.
Terms
Ray
Endpoint
Labels
Diagrams
A capital letter,
C and D
It’s endpoint and any other
point on the ray
Opposite Rays
Segment
The common endpoint and any
other point on each ray
The two endpoints
Term
Definition
is the part of a line
consisting of two points,
and all points between
them.
Labels/Name
Diagram
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.
2
SWBAT: Identify, name, and draw points, lines, segments, rays, and planes.
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.
3
SWBAT: Identify, name, and draw points, lines, segments, rays, and planes.
Homework: pg 9 Numbers 1-21
Homework: Page 9, #'s 1 - 21
4
SWBAT: Use the length and midpoint of a segment to calculate the missing lengths.
Chapter 1 – 2
Warm – Up
Notes:
5
SWBAT: Use the length and midpoint of a segment to calculate the missing lengths.
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.
6
SWBAT: Use the length and midpoint of a segment to calculate the missing lengths.
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.
7
SWBAT: Use the length and midpoint of a segment to calculate the missing lengths.
Example 3: Using Midpoints to Find Lengths
Practice:
Challenge:
8
SWBAT: Use the length and midpoint of a segment to calculate the missing lengths.
9
SWBAT: Use the length and midpoint of a segment to calculate the missing lengths.
Homework: Page 17, #'s 3, 4, 6, 7, 9, 10, 15, 17, 18
10
SWBAT: Name, classify and calculate the measure of angles.
Chapter 1 – 3
Warm – Up
U is the midpoint of TV, TU = 3x + 4,
and UV = 5x - 2. Find TU, UV, and TV.
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.
11
SWBAT: Name, classify and calculate the measure of angles.
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.
12
SWBAT: Name, classify and calculate the measure of angles.
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.
13
SWBAT: Name, classify and calculate the measure of angles.
QS bisects PQR, m PQS = (5y – 1)°, and
m PQR = (8y + 12)°. Find m PQS.
Homework
Holt: pages 24- 27 #'s 9-10, 17-18, 29-31,& 41 - 43
14
SWBAT identify adjacent, vertical, complementary, supplementary and calculate the measures of pairs of angles.
Warm Up:
Pairs of Angles
Adjacent angles:
Linear pair:
a)
a)
b)
b)
Use the diagram below for questions 1 and 2.
1. Identify angles those are only adjacent.
2. Identify angles that are not adjacent.
15
SWBAT identify adjacent, vertical, complementary, supplementary and calculate the measures of pairs of angles.
Use the diagram below for question 3.
3. Identify angles that are adjacent and form a linear pair.
Complementary angles:
Supplementary angles:
16
SWBAT identify adjacent, vertical, complementary, supplementary and calculate the measures of pairs of angles.
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.
17
SWBAT identify adjacent, vertical, complementary, supplementary and calculate the measures of pairs of angles.
8) If the m ABC = (4x – 10)o, and m CBD = (2x + 40)o then what is x,
A
B
m ABC and m CBD?
x = _____ o
m ABC = _____ o
m CBD = _____ o
C
D
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 mAEC  5x  20 and mBED  x  50,
find, in degrees, mCEB.
18
SWBAT identify adjacent, vertical, complementary, supplementary and calculate the measures of pairs of angles.
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.
19
SWBAT: apply the formulas for midpoint and distance in conjunction with the Pythagorean Theorem to find the length of
a line segment.
Chapter 1 – 6
Warm – Up
1. Find CD.
2.
3. Find the missing side length.
Example 1:
a.
b.
20
SWBAT: apply the formulas for midpoint and distance in conjunction with the Pythagorean Theorem to find the length of
a line segment.
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.
21
SWBAT: apply the formulas for midpoint and distance in conjunction with the Pythagorean Theorem to find the length of
a line segment.
Example 3:
a.
b.
Practice:
a.
b.
c.
d.
22
SWBAT: apply the formulas for midpoint and distance in conjunction with the Pythagorean Theorem to find the length of
a line segment.
Homework
23
Geometry – Chapter 1
Practice Test
Name__________________________
Date___________________________
WORKSPACE
intersect,
15. In the accompanying figure, two lines
intersect, m<1 = (4x – 20)°, and
m<3 = (2x – 40)°. Find the number of
degress in m<2.