1 / 11

Beginning Proofs

Beginning Proofs. Lesson 1.4 Two-Column Proofs & Theorems. Theorem : a mathematical statement that can be proven. Theorem Procedures to follow:. We present a theorem or theorems. We prove the theorem(s) We shall omit the proofs of certain theorems, even though all have proofs.

jjessi
Download Presentation

Beginning Proofs

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Beginning Proofs Lesson 1.4 Two-Column Proofs & Theorems

  2. Theorem: a mathematical statement that can be proven.

  3. Theorem Procedures to follow: • We present a theorem or theorems. • We prove the theorem(s) We shall omit the proofs of certain theorems, even though all have proofs.

  4. 3. We use the theorems to help prove sample problems. 4.You are then given the challenge of using the theorems to prove homework problems. Theorems will save you much time if you learn them and then use them!

  5. Theorem 1 If two angles are right angles, then they are congruent. Given: <A is a right angle <B is a right angle Prove: <A is congruent to <B A B

  6. Set Up for Proof Statements <A is right < m<A = 90 <B is right < m<B = 90 <A congruent <B Reasons Given If right < then 90 Given If right < then 90 If 2 angles have the same measure, then they are congruent.

  7. Theorem 2 If two angles are straight angles, then they are congruent. Given: <ABC is a straight angle <DEF is a straight angle Prove: <ABC is congruent to <DEF B C A E F D

  8. Proof Reasons Given If < is straight then m=180˚ Given Same as #2 If 2 angles have the same measure, then they are congruent. Steps 2&4 Statements <ABC is straight < m<ABC = 180˚ <DEF is straight < m<DEF = 180˚ <ABC congruent <DEF

  9. Solve with a partner • The Archimedean Club of Higher Mathematics is planning its annual banquet. The club gives awards to members of 5, 10, and 15 years. The club’s officers, Mrs. Martinez, Mr. Washington, and Ms. Chung, are due to receive awards. From the following information, which award will each receive and which post does each hold?

  10. More information… • Ms. Chung has been a member for 10 years. • The president has been a member for fewer years than Ms. Chung. • Mrs. Martinez has been a member for more years than the secretary.

  11. Answer… • Mrs. Martinez is the vice-president and has been a member for 15 years. • Mr. Washington is the president and has been a member for 5 years. • Ms. Chung is the secretary and has been a member for 10 years.

More Related