Download Lesson 2/3: Segments and Angles

WARM UP
1. Points that lie on the same line are called _________________ points.
2. Solve for 𝑥: 5𝑥 + 6 = 2𝑥 − 5
3. Simplify: 5 2𝑥 − 6 + 3𝑥 − 7
LESSON 2/3: SEGMENTS
AND ANGLES
Geometry
VOCABULARY: SEGMENTS
• Segment: part of a line that has two endpoints
• Congruent: same shape and size
• Congruent segments: segments that have the same length
• Reflexive Property: 𝐴𝐵 ≅ 𝐴𝐵
• Symmetric Property: If 𝐴𝐵 ≅ 𝐶𝐷, then 𝐶𝐷 ≅ 𝐴𝐵
• Transitive Property: If 𝐴𝐵 ≅ 𝐶𝐷 and 𝐶𝐷 ≅ 𝐸𝐹, then 𝐴𝐵 ≅ 𝐸𝐹
• Postulate: accepted as true without proof
• Midpoint: the point that divides a segment in half
VOCABULARY: ANGLES
• Ray: part of a line that starts at an endpoint and extends infinitely in one
direction
• Opposite rays: two rays that have a common end point and form a line
• Angle: a figure formed by two rays with a common endpoint
• Vertex: the common endpoint in an angle
• Sides: the rays that form an angle
• Degrees: a unit of measurement for angles; 1 𝑑𝑒𝑔𝑟𝑒𝑒 =
•
•
•
•
1
𝑜𝑓
360
𝑎 𝑐𝑖𝑟𝑐𝑙𝑒
Acute: angle with measure greater than 0° and less than 90°
Obtuse: angle with measure greater than 90° and less than 180°
Right: angle with measure of 90°
Straight: angle with measure of 180°
ANGLE ADDITION POSTULATE
• If point D is in the interior of angle ABC, then 𝑚∠𝐴𝐵𝐷+𝑚∠𝐷𝐵𝐶 = 𝑚∠𝐴𝐵𝐶
A
D
B
C
EXAMPLE
Use the diagram to classify and find the measure of each angle.
a. ∠𝐴𝐹𝐶
C
b. ∠𝐶𝐹𝐷
B
c. ∠𝐵𝐹𝐷
D
d. ∠𝐴𝐹𝐷
36°
36°
A
F
E
EXAMPLE
If 𝐿𝐽 bisects ∠𝐼𝐿𝐾, what is the measure of ∠𝐺𝐿𝐽
I
J
H
36°
G
L
K
EXAMPLE
Jackson said, “Congruent segments are the same as equal segments.” Explain
how he has misunderstood congruence and equality.
HOMEWORK QUESTIONS
CORRECTING HOMEWORK
• Get your homework out so I can stamp it.
• If you do not have your homework complete, write your name on the board.
• Use red pen/pencil to correct.
• Trade with someone who has the homework done.
• If you didn’t get it done, you need to be working on finishing it now.
Remember no cheating and no work = no credit.
• Make sure you write CB with your name or you will lose your citizenship points
for today.
HOMEWORK
• 1st and 2nd hour: Lesson 3 #1-30
• 3rd hour: Lesson 3 #1-30 ODD