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Five-Minute Check (over Lesson 2–6) CCSS Then/Now Postulate 2.8: Ruler Postulate Postulate 2.9: Segment Addition Postulate Example 1: Use the Segment Addition Postulate Theorem 2.2: Properties of Segment Congruence Proof: Transitive Property of Congruence Example 2: Real-World Example: Proof Using Segment Congruence Lesson Menu

A. Distributive Property B. Addition Property C. Substitution Property State the property that justifies the statement. 2(LM + NO) = 2LM + 2NO A. Distributive Property B. Addition Property C. Substitution Property D. Multiplication Property 5-Minute Check 1

A. Distributive Property B. Substitution Property C. Addition Property State the property that justifies the statement. If mR = mS, then mR + mT = mS + mT. A. Distributive Property B. Substitution Property C. Addition Property D. Transitive Property 5-Minute Check 2

A. Multiplication Property B. Division Property State the property that justifies the statement. If 2PQ = OQ, then PQ = A. Multiplication Property B. Division Property C. Distributive Property D. Substitution Property 5-Minute Check 3

State the property that justifies the statement. mZ = mZ A. Reflexive Property B. Symmetric Property C. Transitive Property D. Substitution Property 5-Minute Check 4

C. Substitution Property D. Transitive Property State the property that justifies the statement. If BC = CD and CD = EF, then BC = EF. A. Reflexive Property B. Symmetric Property C. Substitution Property D. Transitive Property 5-Minute Check 5

Which statement shows an example of the Symmetric Property? A. x = x B. If x = 3, then x + 4 = 7. C. If x = 3, then 3 = x. D. If x = 3 and x = y, then y = 3. 5-Minute Check 6

G.CO.9 Prove theorems about lines and angles. Content Standards G.CO.9 Prove theorems about lines and angles. G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Mathematical Practices 2 Reason abstractly and quantitatively. 3 Construct viable arguments and critique the reasoning of others. CCSS

You wrote algebraic and two-column proofs. Write proofs involving segment addition. Write proofs involving segment congruence. Then/Now

Reflexive Property Equality Congruence

I am as tall as myself.

Symmetric Property Equality: Congruence:

If I am as tall as my brother, my brother is as tall as me.

Transitive Property Equality: Congruence:

If I am as tall as my brother, and my brother is as tall as my cousin, I am as tall as my cousin.

REMEMBER 123… RST COMPARING 1 THING is REFLEXIVE COMPARING 2 THINGS is SYMMETRIC COMPARING 3 THINGS is TRANSITIVE 1-4 Solving Equations

Concept

Definition of a Midpoint of a Segment

Bisector of a Segment   F l G M H

Ex. Writing a proof: Given: 2AB = AC Prove: AB = BC A B C 2AB = AC Copy or draw diagrams and label given info to help develop proofs Ex. Writing a proof: Given: 2AB = AC Prove: AB = BC A B C Statements Reasons 2AB = AC AC = AB + BC 2AB = AB + BC AB = BC Given Seg. Add Pos Trans. Or subst. Subtr. Prop.

Given: Prove: Statements Reasons 1. 2. 3. 4. 5. Example 2

Use the Segment Addition Postulate Proof: Statements Reasons Example 1

Given: AC = AB ; AB = BX; CY = XD Prove: AY = BD Prove the following. Given: AC = AB ; AB = BX; CY = XD Prove: AY = BD Statements Reasons Example 1

HOMEWORK Pg. 147 1,2&4

End of the Lesson