# "The Basics of Proof Writing: Defining, Identifying, and Solving with Theorems" In this lesson, you will learn what a proof is and how to construct a proof for a given hypothesis and conclusion. You will also become familiar with  ﻿Slide1this lesson defines what a proof is and shows how to write aproof for a given hypothesis and conclusions. You will be able to identify the postulates, axioms, and theorems that justify the statements in a

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## About "The Basics of Proof Writing: Defining, Identifying, and Solving with Theorems" In this lesson, you will learn what a proof is and how to construct a proof for a given hypothesis and conclusion. You will also become familiar with

PowerPoint presentation about '"The Basics of Proof Writing: Defining, Identifying, and Solving with Theorems" In this lesson, you will learn what a proof is and how to construct a proof for a given hypothesis and conclusion. You will also become familiar with'. This presentation describes the topic on ﻿Slide1this lesson defines what a proof is and shows how to write aproof for a given hypothesis and conclusions. You will be able to identify the postulates, axioms, and theorems that justify the statements in a. The key topics included in this slideshow are . Download this presentation absolutely free.

## Presentation Transcript

Slide1this lesson defines what a proof is and shows how to write aproof for a given hypothesis and conclusions.

Slide2You will be able to identify the postulates, axioms, and theorems that justify the statements in a proof.  You will be able to use a theorem to solve problems.

Slide3Theorem:  A cat has nine tails.   Proof:   No cat has eight tails.  A cat has one tail more than no cat.  Therefore, a cat has nine tails.

Slide4Proof –  A series of true statements leading to a desired conclusion  Theorem –  A statement that can be proven true  Given –  Specified  Prove –  To show that a conclusion is true

Slide5If Angles are vertical angles, then their measures are equal.  To start a proof, clearly state what is  given  and is to  prove .  Given or hypothesis: “angles are vertical”  Conclusion:  “their measures are equal”

Slide6Next, draw a picture of the given.                                                                  a                                                 b                    c                               l                               d                                                                                        m   a and   d are vertical angles     c and   b are vertical angles

Slide7To Prove:  m   a = m    d  m   c = m    b  Work in 2 columns.  You are now ready.

Slide8Statement  Lines  l  &  m intersect to form vertical angles a & d  m  a  + m   b = 180 o  m    d + m    b = 180 o Proof 1. Given 2.  a &   b are adjacent on m  and are supplementary 3.  b and   d are adjacent on l  and are supplementary

Slide9m  a +  m  b =  m  b  +  m  d    m  a =  m  d 4) Axiom I, substitution and steps 2 & 3 5) Axiom 3, if equals are subtracted from equals, the differences are equal