daily warm-up
DESCRIPTION
Daily Warm-Up. Daily Warm-Up. Given : m 1 = m 3 Prove : m 1 + m 2 = m 2 + m 3. Reasoning in Algebra. During this lesson, you will write simple algebraic proofs using angle and segment addition postulates. Recall : Angle Addition Postulate. - PowerPoint PPT PresentationTRANSCRIPT
Daily Warm-Up
STATEMENT REASON1. m 1 = m 3 and m 3 = m 5∠ ∠ ∠ ∠ 1. Given2. ______________________ 2. ______________________ 1. ABC DEF 1. Given2. ______________________ 2. ______________________ 1. m A = 105 and mE = 105 1. Given2. ______________________ 2. ______________________ 1. X Y and Y Z 1. Given2. ______________________ 2. ______________________ 1. OG = 9; RE = 9 1. Given2. ______________________ 2. ______________________
Mrs. McConaughy Geometry 1
Daily Warm-Up
Mrs. McConaughy Geometry 2
STATEMENT REASON1. m A = m B and m B = m C∠ ∠ ∠ ∠ 1. Given2. ______________________ 2. ______________________ 1. BIG MAN 1. Given2. ______________________ 2. ______________________ 1. m 1 = 97and m2 = 97 1. Given2. ______________________ 2. ______________________ 1. 1 7 and 7 9 1. Given2. ______________________ 2. ______________________ 1. GO = 18; UP = 18 1. Given2. ______________________ 2. ______________________
Given: m 1 = m 3Prove: m 1 + m 2 = m 2 + m 3
Reasoning in Algebra
During this lesson, you will write simple algebraic proofs using angle and segment addition postulates.
Mrs. McConaughy Geometry 3
Recall: Angle Addition Postulate
If D is in the interior of ABC, ∠then _____________________.
Mrs. McConaughy Geometry 4
A
D
B C
Recall: Segment Addition Postulate
If M is between collinear points A and Y, then ______________.
Mrs. McConaughy Geometry 5
AM + MY = AY
Y
MA
Example 1
Given: m ∠ DOF = 124, m ∠ DOE = 36. Find m ∠ EOF.
O D
E
F
Mrs. McConaughy Geometry 6
Labeling Angles Using Numbers
Mrs. McConaughy Geometry 7
∠ 1 = _____
∠ 2 = _____
∠ 3 = _____
C D
A
B
O
132
Reflexive Property of Congruence
Mrs. McConaughy Geometry 8
A A and AB AB for any angle A and any segment AB.
You will use the reflexive property in many proofs.
Example 2: Writing a Simple Proof
Given:
m 1 = m 3∠ ∠Prove:
m WOY = m ZOX ∠ ∠
Mrs. McConaughy Geometry 9
32
1
Z
Y
X
W
Mrs. McConaughy Geometry 10
Statement Reason
1. 1.
2. 2.
3. 3.
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5. 5.
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Example 3: Writing a Simple Proof
Given:
AB = CD
Prove:
AC = BD
Mrs. McConaughy Geometry 11
D
C
B
A
Mrs. McConaughy Geometry 12
Statement Reason
1. 1.
2. 2.
3. 3.
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Homework Assignment
Supplemental WS: Angle and Segment Addition 1-17 all.
Mrs. McConaughy Geometry 13