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1.4 Beginning Proofs

Learn how to present & prove theorems step by step in a book. Essential theorems for homework. Diagram & reasons included.

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1.4 Beginning Proofs

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  1. 1.4 Beginning Proofs

  2. Theorem Procedure in the Book • They will present the theorem • They will prove the theorem • They will use the theorem to prove other problems • You will use the theorem in homework problems • YOU MUST KNOW THESE THEOREMS!!!

  3. Proof Procedure • Draw the diagram (if there is one) • Set up the two-columns • Write the givens (sometimes they will not go side by side) • Use definitions and theorems to prove the conclusion • The conclusion should be the last statement

  4. Theorem 1 A If two angles are right angles, then they are congruent Given: Angle A is a right angle Angle B is a right angle Prove: Angle A is congruent to Angle B Statements Reasons__________ 1. Angle A is a right angle Given 2. m<A = 90 If an angle is a right angle, then its measure is 90 3. Angle B is a right angle Given 4. m< B= 90 Same as 2 5. <A = <B If two angles have the same measure, then they are congruent B

  5. Theorem 2 If two angles are straight angles, then they are congruent Given: Angle ABC is a straight angle Angle DEF is a straight angle Prove: <ABC is congruent to <DEF Statements Reasons__________ • ABC is a straight angle Given • m <ABC = 180 If an angle is a straightangle, then its measure is 190 • 3. DEFis a straight angle Given • 4. m <DEF = 180 Same as 2 • 5. <ABC = < DEF If two angles have the same measure, then they are congruent A B C D E F

  6. Given: Angle A is a right angle Angle C is a right angle Prove: Angle A is congruent to Angle C Statements Reasons__________ • Angle A is a right angle Given • 2. Angle C is a right angle Given 3. <A = <CIf two angles are right angles, then they are congruent (Thm 1) A B D C

  7. Given: Diagram as shown Prove: <EFG = <HFJ Statements Reasons__________ • Diagram as shown Given • 2. <EFG is a straight angle Assumed from diagram 3. <HFJ is a straight angle Assumed from diagram • <EFG = < HFJ If two angles are straight angles, • then they are congruent (Thm 2) E J F H G

  8. Given: <RSV = 50 <TSV = 40 Angle X is a right angle Prove: <RST = < X Statements Reasons__________ • <RSV = 50 Given • 2. <TSV = 40 Given • <RST = 90 Addition (50+40=90) • 4. <RST is a right angle If an angle is a 90 angle, it is a right • angle • 5. X is a right angle Given • 6. <RST = <X If two angles are right angles, then they are congruent R V X S T

  9. Statements We Will Use To Prove page • If two angles have the same measure, then they are congruent • If an angle equals 90/180, then it is a right/straight angle. • If two angles are right angles, then they are congruent • If two angles are straight angles, then they are congruent

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