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

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Presentation transcript:

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

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. Introducing…

1.We present a theorem(s). 2.We prove the theorem(s). 3.We use the theorems to help prove sample problems. 4. You use the theorems to prove homework problems. Theorem Procedure… Note: The sooner you learn the theorems, the easier your homework will be!

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

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

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! Practice Makes Perfect…

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

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

Lesson 1.4 Worksheet Homework