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Geom25ProvingSegmentsAnglesNotes.notebook
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Geometry
P11 25 Proving Statements about Segments and Angles
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A _______________ is a logical argument that use deductive reasoning to show that a statement is true.
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SJ P54
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SJ P5455
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SJ P58
Geom25ProvingSegmentsAnglesNotes.notebook
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Word BankM is the midpoint of RT
Def. of MIdpoint
Transitive
MT = RS + SM
Segment Addtion
RM = MT
Given
RS + SM = RM
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HW11 #25 WS
Please put your name and class period at the top ofthe homework. Also include the homework number.
Warm Up
Find the complement and the supplement of the angle measure.
1. 59° 2. 20° 3. 53°
Cumulative Warm Up
Use the figure.1. Name a pair of adjacent complementary angles.
2. Find m∠AEC.
3. Find m∠AED.
4. Find m∠BED.
Exploration 1
Four steps of a proof are shown. Write the reasons for each statement.
Given AC = AB + ABProve AB = BC
Geom25ProvingSegmentsAnglesNotes.notebook
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Exploration 2
Six steps of a proof are shown.
Complete the statements that correspond to each reason.
Given m∠1 = m∠3
Prove m∠EBA = m∠CBD
Example 1
Write a twocolumn proof for the situation in Example 4 from the Section 2.4 lesson.
Given m∠1 = m∠3
Prove m∠DBA = m∠EBC
Monitoring Progress 1
Six steps of a twocolumn proof are shown. Copy and complete the proof.
Given T is the midpoint of .Prove x = 5
Theorem
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Name the property that the statement illustrates.
a. If ∠T ≅ ∠V and ∠V ≅ ∠R, then ∠T ≅ ∠R.
b. If , then .
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Example 3
Write a twocolumn proof for the
Symmetric Property of Segment Congruence.
Given Prove
Example 4
Prove this property of midpoints: If you know that M is the midpoint of , prove that AB is two times AM and AM is onehalf AB.
Given M is the midpoint of .Prove AB = 2AM,
Concept Summary