Presentation on theme: "1. If the measures of two angles are ?, then the angles are congruent. 2. If two angles form a ?, then they are supplementary. 3. If two angles are complementary."— Presentation transcript:
1. If the measures of two angles are ?, then the angles are congruent. 2. If two angles form a ?, then they are supplementary. 3. If two angles are complementary to the same angle, then the two angles are ?. equal linear pair congruent Warm-Up
flowchart proof paragraph proof Vocabulary A second style of proof is a flowchart proof, which uses boxes and arrows to show the structure of the proof. The justification for each step is written below the box.
This next theorem should be a part of your theorem notebook – be sure to title it, write the theorem itself, illustrate and prove it in your notebook …. Make a plan … how would you prove this? 60 seconds to discuss -
Who can walk me through what their group has done?
Let’s take this example of a flowchart and rewrite it as a two-column proof Talk it out with your table … how would you prove this?
StatementsReasons 1. 2.2.. 3..3. 4. 5. Given Def. of comp. angles Substitution Def. of comp. angles
With your table, outline a proof -
StatementsReasons 1. 2.2.. 3..3. 4. 5. Given Addition Prop of = Substitution Segment Add. Postulate
Prove: 2AB = AC Given: B is the midpoint of AC. With your table, outline a proof -
The last type I will introduce is a paragraph proof. In this style, the steps of the proof and their matching reasons are presented as sentences in a paragraph. The book will tell you this style of proof is less “formal” than a two-column proof (and then say you still must include every step). In my mind, these are the most useful. The first type of proof we introduced was the two column proof – it is the type that is typically used in high school geometry courses. One column has statements, the other the reasons – easy to understand, organized, and outside of geometry, essentially useless. Today we also introduced flowchart proofs. I hate them. However, that doesn’t mean they’re not valid or useful. But it does mean I hate them.
Two new theorems for your notebook – title, definition, illustration and proof …
Theorem 2-7-2Vertical Angles Theorem Vertical angles are congruent. With your table, trying writing a proof that would show vertical angles are equal. You may use two column, flowchart or paragraph proof. Remember when proving a theorem we can only rely on definitions, postulates and theorems we have previously proven.
StatementsReasons 1. 2. 2.. 3..3. 4. 5. 6. 7.
With your table, construct a proof in the style of your choosing
Lesson Quiz Write either a two- column proof, a flowchart or a paragraph proof