Chapter 2 Segments and Angles · 2019-09-20 · Segments and Angles. Section 6 Properties of...
Transcript of Chapter 2 Segments and Angles · 2019-09-20 · Segments and Angles. Section 6 Properties of...
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Chapter 2
Segments and Angles
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Section 6Properties of Equality and Congruence
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The photos to the left illustrate the Reflexive, Symmetric, and Transitive Properties of Equality. You can use these properties in geometry with statements about equality and congruence.
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Example 1: Name Properties of Equality and Congruence
Name the property that the statement illustrates.
a. If GH ≅ JK then JK ≅ GH.
symmetric
b. DE = DE
reflexive
c. If <P ≅ <Q and <Q ≅ <R, then <P ≅ <R.
transitive
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Checkpoint: Name Properties of Equality and Congruence
Name the property that the statement illustrates.
1. If DF = FG and FG = GH, then DF = GH.
transitive
1. <P ≅ <P
reflexive
1. If m<S = m<T, then m<T = m<S.
symmetric
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Logical Reasoning In geometry, you are often asked to explain why statements are true. Reasons can include definitions, theorems, postulates or properties.
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Example 2: Use Properties of Equality
In the diagram, N is the midpoint of MP, and P is the midpoint of NQ. Show that MN = PQ.
MN = NP ___Definition of midpoint____________
NP = PQ ___Definition of midpoint____________
MN = PQ ___Transitive Property_______________
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Checkpoint: Use Properties of Equality and Congruence
<1 and <2 are vertical angles, and <2 ≅ <3. Show that <1 ≅ <3.
<1 ≅ <2 ___Vertical Angles___ Theorem
<2 ≅ <3 Given
<1 ≅ <3 __Transitive__ Property of Congruence
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Example 3: Justify the Congruent Supplements Theorem
<1 and <2 are both supplementary to <3. Show that <1 ≅ <2.
1)
2)
3)
4)
5)
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Checkpoint: Use Properties of Equality and Congruence
In the diagram, M is the midpoint of AB. Show that AB = 2 × AM.
MB = AM Definition of ___midpoint____
AB = AM + MB ____Segment Addition____ Postulate
AB = AM + AM __Substitution__ Property of Equality
AB = 2 × AM Distributive Property (simplify)