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Lesson 1.4 Beginning Proofs

Lesson 1.4 Beginning Proofs. Objective: Write simple two-column proofs. Introducing…. The Two-Column Proof! The two-column proof is the major type of proof we use throughout our studies. Def. A theorem is a mathematical statement that can be proved. Theorem Procedure….

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Lesson 1.4 Beginning Proofs

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  1. Lesson 1.4 Beginning Proofs Objective: Write simple two-column proofs

  2. Introducing… The Two-Column Proof! The two-column proof is the major type of proof we use throughout our studies. Def. A theorem is a mathematical statement that can be proved.

  3. Theorem Procedure… • We present a theorem(s). • We prove the theorem(s). • We use the theorems to help prove sample problems. • You use the theorems to prove homework problems. Note: The sooner you learn the theorems, the easier your homework will be! 

  4. Theorem 1 If two angles are right angles, then they are congruent. Given: <A is a right <. <B is a right <. Prove: B A Statement Reason 1. <A is a right < 1. Given 2. m<A = 90° 2. If an < is a right < then its measure is 90° 3. <B is a right < 3. Given 4. If an < is a right < then its measure is 90° 4. m<B = 90° • If 2 <‘s have the same measure then they are congruent. 5.

  5. Theorem 2 If two angles are straight angles, then they are congruent. U Given: <NAU is a straight <. <PHS is a straight <. Prove: A N P H S Statement Reason

  6. Practice Makes Perfect… Now that we know the two theorems (and have proved them), we apply what we know to sample problems. about what we can and cannot assume from a diagram! This is important with proofs!

  7. Example #1 Given: <RST = 50° <TSV = 40° <X is a right angle Prove: R T X S V Statement Reason

  8. Example #2 Given: <ABD = 30° <ABC = 90° <EFY = 50° 20’ <XFY = 9° 40’ Prove: X Y D A F E B C Statement Reason

  9. Euclid’s 5 Postulates • A straight line segment can be drawn joining any two points • Any straight line segment can be extended indefinitely in a straight line • Given any straight line segment, a circle can be drawn having the segment as the radius and one endpoint as the center • All right angles are congruent • If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough Video: https://youtu.be/fv-mDpscZlo

  10. Homework Lesson 1.4 Worksheet

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