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1.4 Beginning Proofs

1.4 Beginning Proofs. 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!!!. Proof Procedure.

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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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