Using Congruent Triangles
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Presentation Transcript
Using Congruent Triangles Chapter 4
Objective List corresponding parts. Prove triangles congruent (ASA, SAS, AAS, SSS, HL) Prove corresponding parts congruent (CPCTC) Examine overlapping triangles.
Key Vocabulary - Review Reflexive Property Vertical Angles Congruent Triangles Corresponding Parts
Review: Congruence Shortcuts **Right triangles only: hypotenuse-leg (HL)
Congruent Triangles (CPCTC) Two triangles are congruent triangles if and only if the corresponding parts of those congruent triangles are congruent. Corresponding sides are congruent Corresponding angles are congruent
Example: Name the Congruence Shortcut or CBD SAS ASA SSA CBD SSS
Name the Congruence Shortcut or CBD Vertical Angles Reflexive Property SAS SAS Reflexive PropertySSA Vertical Angles SAS CBD
Your Turn: Name the Congruence Shortcut or CBD
Your Turn: Name the Congruence Shortcut or CBD
Your Turn: Name the Congruence Shortcut or CBD
Example Indicate the additional information needed to enable us to apply the specified congruence postulate. B AC For ASA: For SAS: A For AAS:
Your Turn: Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: For SAS: For AAS:
Using Congruent Triangles: CPCTC If you know that two triangles are congruent, then you can use CPCTC to prove the corresponding parts in whose triangles are congruent. *You must prove that the triangles are congruent before you can use CPCTC*
Example 1 Use Corresponding Parts In the diagram, AB and CD bisect each other at M. Prove that A B.
Example 1 Use Corresponding Parts Statements 1. AB and CD bisect each other at M. Reasons Given 1. 2. 2. 3. 3. 4. 4. 5. 5. 6. 6.
The Proof Game! Here s your chance to play the game that is quickly becoming a favorite among America s teenagers: The Proof Game!
Rules: 1. Guys vs. Gals 2. Teams must take turns filling in the statements and reasons in the proofs to come. 3. If the statement/reason combo is correct, team gets 1 point. Next team continues. 4. If the statement/reason combo is incorrect, team loses 1 point. Next team fixes mistake. 5. Teammates cannot help the person at the board he/she is on their own. Cheating loses all points!!
Number One Given: ABD = CBD, ADB = CDB Prove: AB = CB B A C Statement Reason D
Number Two Given: MO = RE, ME = RO Prove: M = R O R Statement Reason M E
Number Three Given: SP = OP, SPT = OPT Prove: S = O O T S Statement Reason P
Number Four Given: KN = LN, PN = MN Prove: KP = LM K L N Statement Reason M P
Number Five Given: C = R, TY = PY Prove: CT = RP C R Y Statement Reason P T
Number Six Given: AT = RM, AT || RM Prove: AMT = RTM A T Statement Reason M R
Example 2 Visualize Overlapping Triangles Sketch the overlapping triangles separately. Mark all congruent angles and sides. Then tell what theorem or postulate you can use to show JGH KHG. SOLUTION 1. Sketch the triangles separately and mark any given information. Think of JGHmoving to the left and KHGmoving to the right. Mark GJH HKG and JHG KGH.
Example 2 Visualize Overlapping Triangles 2. Look at the original diagram for shared sides, shared angles, or any other information you can conclude. In the original diagram, GH and HG are the same side, so GH HG. Add congruence marks to GHin each triangle. 3. You can use the AAS Congruence Theorem to show that JGH KHG.
Example 3 Use Overlapping Triangles Write a proof that shows AB DE. ABC DEC CB CE AB DE SOLUTION
Use Overlapping Triangles Your Turn: Redraw the triangles separately and label all congruences. Explain how to show that the triangles or corresponding parts are congruent. GivenKJ KLand J L,show NJ ML.
Use Overlapping Triangles Your Turn: Given SPR QRPand Q S, show PQR RSP. 3.
Joke Time What happened to the man who lost the whole left side of his body? He is all right now. What did one eye say to the other eye? Between you and me something smells.
Upcoming Schedule Quiz on Friday HL, proofs, CPCTC, Isosceles Triangle Thm, overlapping triangles Monday vocabulary terms Tues Practice Day Wednesday Chapter 4 Test **reminder projects due Oct. 27!!!
