Download lesson 1.3 Geometry.notebook

lesson 1.3 Geometry.notebook
September 12, 2015
Warm Up
1. S is between A and B. If AS = 12 and AB = 34, what is the length of SB?
2. M is the midpoint of AB. AM = 2y and AB = 8y ­ 8. find the length of AM, MB, and AB. lesson 1.3 Geometry.notebook
September 12, 2015
lesson 1.3 Geometry.notebook
September 12, 2015
lesson 1.3 Geometry.notebook
September 12, 2015
lesson 1.3 Geometry.notebook
September 12, 2015
lesson 1.3 Geometry.notebook
September 12, 2015
lesson 1.3 Geometry.notebook
September 12, 2015
lesson 1.3 Geometry.notebook
GOAL:
acute
September 12, 2015
Name and classify angles.
right
straight
obtuse
lesson 1.3 Geometry.notebook
September 12, 2015
Definitions
lesson 1.3 Geometry.notebook
September 12, 2015
An angle is a figure formed by two rays, or sides, with a common endpoint called the vertex (plural: vertices). You can name an angle several ways: 1. by its vertex 2. by a point on each ray and the vertex
3. or by a number.
S
Vertex
1
R
T
lesson 1.3 Geometry.notebook
September 12, 2015
The set of all points between the sides of the angle is the interior of an angle. The exterior of an angle is the set of all points outside the angle.
Angle Name
∠R, ∠SRT, ∠TRS, or ∠1
lesson 1.3 Geometry.notebook
September 12, 2015
You cannot name an angle just by its vertex if the point is the vertex of more than one angle. In this case, you must use all three points to name the angle, and the middle point is always the vertex.
Z
w
Q
V
lesson 1.3 Geometry.notebook
September 12, 2015
Naming Angles
Name three of the angles.
lesson 1.3 Geometry.notebook
September 12, 2015
Your Turn
Write the different ways you can name the angles in the diagram.
lesson 1.3 Geometry.notebook
September 12, 2015
The measure of an angle is usually given in degrees. Since there are 360° in a circle, one degree is of a circle. When you use a protractor to measure angles, you are applying the following postulate.
lesson 1.3 Geometry.notebook
80
90
100
110
70
60
110
50
100
90
150
160
70
130
140
50
130
140
0
120
80
60
120
40
September 12, 2015
0°
40
150
30
How do you label an angle's measure?
160
20
170
10
180
0
170
137°
180
3
lesson 1.3 Geometry.notebook
September 12, 2015
You can use the Protractor Postulate to help you classify angles by their measure. The measure of an angle is the absolute value of the difference of the real numbers that the rays correspond with on a protractor.
m∠DOC = |d – c| or |c – d|.
lesson 1.3 Geometry.notebook
September 12, 2015
Why do we not classify an angle that is greater than 180o??
lesson 1.3 Geometry.notebook
September 12, 2015
Construct each given angle using your Protractor!!!
1) 93o
Step 1) Draw a ray using a straight edge
2) 28
Step 2) Put the center of your protractor on the endpoint of the ray (vertex). The ray is pointing towards zero!
3) 135o
Step 3) locate the given angle measure and draw a point
o
Step 4) connect the point with the vertex
80
90
100
110
120
70
60
100
90
140
50
120
40
130
40
130
70
60
110
50
80
150
6°
140
30
160
30
150
107°
20
170
20
160
10
170
0
180
10
0
180
lesson 1.3 Geometry.notebook
Measuring and Classifying Angles
Find the measure of each angle. Then classify each as acute, right, or obtuse.
A. ∠WXV
B. ∠ZXW
September 12, 2015
lesson 1.3 Geometry.notebook
September 12, 2015
Measuring and Classifying Angles
Use the diagram to find the measure of each angle. Then classify each as acute, right, or obtuse.
a. m∠BOA b. m∠DOB c. m∠EOC
lesson 1.3 Geometry.notebook
September 12, 2015
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.
lesson 1.3 Geometry.notebook
September 12, 2015
lesson 1.3 Geometry.notebook
September 12, 2015
The Angle Addition Postulate is very similar to the Segment Addition Postulate that you learned in the previous lesson.
lesson 1.3 Geometry.notebook
September 12, 2015
Using the Angle Addition Postulate
m∠DEG = 115°, and m∠DEF = 48°. Find m∠FEG
m∠DEG = m∠DEF + m∠FEG
lesson 1.3 Geometry.notebook
September 12, 2015
Your Turn
m∠XWZ = 121° and m∠XWY = 59°. Find m∠YWZ.
lesson 1.3 Geometry.notebook
September 12, 2015
An angle bisector is a ray that divides an angle into two congruent angles.
JK bisects ∠LJM; thus ∠LJK ≅ ∠KJM. lesson 1.3 Geometry.notebook
September 12, 2015
KM bisects ∠JKL, m∠JKM = (4x + 6)°, and m∠MKL = (7x – 12)°. Find m∠JKM.
lesson 1.3 Geometry.notebook
September 12, 2015
Your Turn
QS bisects ∠PQR, m∠PQS = (5y – 1)°, and
m∠PQR = (8y + 12)°. Find m∠PQS.
step 1: Draw the figure
step 2: solve for y
P
S
Q
R
step 3: answer the question
lesson 1.3 Geometry.notebook
September 12, 2015
Your Turn! Again!
JK bisects ∠LJM, m∠LJK = (­10x + 3)°, and
m∠KJM = (–x + 21)°. Find m∠LJM.
lesson 1.3 Geometry.notebook
September 12, 2015
ClassWork
Classify each angle as acute, right, or obtuse.
1. ∠XTS
acute
2. ∠WTU
right
3. K is in the interior of ∠ LMN, m∠ LMK =52°, and m∠ KMN = 12°. Find m∠ LMN.
64°
4. BD bisects ∠ABC, m∠ABD = , and m∠DBC = (y + 4)°. Find m∠ABC. 32°
5. m∠WYZ = (2x – 5)° and m ∠XYW = (3x + 10)°. Find the value of x.
x=35
6. Use a protractor to draw an angle with a measure of 165°.
lesson 1.3 Geometry.notebook
Homework: Due next class
1.3 pg 24 #12­18, 30­32
Quiz: 1.1­1.3 Now!!
September 12, 2015
lesson 1.3 Geometry.notebook
September 12, 2015