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Module 5 Lesson 2 – Part 2 Writing Proofs

Module 5 Lesson 2 – Part 2 Writing Proofs. Proving Triangles Congruent (Remember to print the Learning Guide notes that go with this lesson so you can use them as you follow along.). You have studied proofs in earlier modules. Remember that you always start with the given information.

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Module 5 Lesson 2 – Part 2 Writing Proofs

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  1. Module 5 Lesson 2 – Part 2Writing Proofs Proving Triangles Congruent (Remember to print the Learning Guide notes that go with this lesson so you can use them as you follow along.)

  2. You have studied proofs in earlier modules. • Remember that you always start with the given information. • MARK that information on the diagrams. This is KEY! That is the only way you will know if it is SSS or SAS, etc. • For each step in the proof, you must give a reason.

  3. Possible reasons • Given • Properties • Reflexive (AB = AB) (very useful when triangles share a side) • Symmetric • Transitive • Definition of _________ • Definition of perpendicular lines • Definition of midpoint • Definition of segment bisector • Definition of angle bisector • Definition of congruent segments • Theorems • Vertical angles are congruent. • All right angles are congruent. • If 2 parallel lines are cut by a transversal, alternate interior angles are congruent. • If 2 parallel lines are cut by a transversal, corresponding angles are congruent. • SSS, SAS, ASA, AAS and HL

  4. 1. Look at the given information and MARK it in the diagram. How do I start a proof?? • What you are given can lead to more steps in the proof (everything is given for a reason!) For example, if you are given an angle bisector, you will have a pair of congruent angles. You need to MARK them in the diagram and also state that the angles are equal in the proof.

  5. 2. Look for shared sides. If the two triangles share a side, MARK THEM IN THE DIAGRAM and state it in the proof. Statement: OM = OM Reason: Reflexive Property

  6. 3. Look for vertical angles. • If you see an X in the diagram anywhere, those are vertical angles. MARK THEM IN THE DIAGRAM and state it in the proof. • Statement: <3 = <4 • Reason: Vertical angles are congruent

  7. 4. You should be ready to finish the proof. • Look at the diagram and all the things you have marked. Now decide if it is SSS, SAS, ASA, AAS or HL. • Statement: Name the triangles (remember to make sure the letters are in the right order). • Example: ∆ABC= ∆ DEF • Reason: Look at the diagram to determine if it is SSS, SAS, ASA, AAS or HL

  8. Ready for some examples?

  9. Given Right angles are congruent. Reflexive Property SAS

  10. Given Defn. of angle bisector Reflexive property SAS

  11. Given Alternate interior angles are congruent. Vertical angles are congruent. ASA

  12. You try some! • There are some “You Try” problems in the learning guide notes. • Try those and then check your answers. • If you have any questions, contact your teacher so that he/she can help you.

  13. Last idea: We know that parts of congruent triangles match up. • For example, if ∆RST = ∆FED, then we know that • RS = FE (since they are the first two letters of each) • <S = <E (since they are the middle letters of each) • TR = DF, etc. This is called CPCTC:Corresponding Parts of Congruent Triangles are Congruent

  14. Last proof! This one will use CPCTC. Notice how it is set up the same, but the “prove” is different. 1 2 Given Vertical angles are congruent SAS CPCTC

  15. You try one more! • There is one more “You Try” problem in the learning guide notes. • Try it (remember it will use CPCTC) and then check your answers. • If you have any questions, contact your teacher so that he/she can help you.

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