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Name _______________________________________________ Date ____________________ Introduction to Geometry What is Proof? Independent Practice 1. Define the following terms. Conjecture: Inductive Reasoning: Deductive Reasoning: Counterexample: 2. Mr. Epstein placed two-stools in front of the classroom. One had three-legs and the other had four legs. He asked Charlene to sit on each of them. She noticed that the four-legged stool rocked when she sat on it, but the three-legged stool was steady and did not rock. Make a conjecture about why this might have occurred. 4. Provide a counterexample to show that the statement is false. You may use words or draw a diagram.

If 𝐴𝐵#### ≅ 𝐵𝐶####,then 𝐵 is the midpoint of 𝐴𝐶####.

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3. Which type of reasoning is being used in each of the following situations? State how you know. It has rained the past 3 days. Joaquin makes a conjecture that it will rain again tomorrow.

Inductive Deductive

Maria is writing a list of numbers. She asked Susanne what the next number would be. After looking at the list: 7, 14, 21, 28, 35, 42, _____ Susanne states, “the next number will be 49.”

Inductive Deductive

Ky adds the sides of an equilateral triangle and finds the length of the perimeter to be 3 times the length of one side. He guesses that the perimeter of every equilateral triangle will be three times the length of a side.

Inductive Deductive

4. Use the diagram to complete the proof by filling in the blanks. Given: 𝑅𝑇#### and 𝑃𝑄#### intersect at point 𝑆 so that 𝑅𝑆 = 𝑃𝑆and 𝑆𝑇 = 𝑆𝑄. Prove: 𝑅𝑇 = 𝑃𝑄

Statements Reasons 1. Given 1. Given

2. 𝑅𝑆 + 𝑆𝑇 = 𝑃𝑆 + 𝑆𝑄 2. Addition Property

3. 𝑅𝑆 + 𝑆𝑇 = 𝑅𝑇; 𝑃𝑆 + 𝑆𝑄 = 𝑃𝑄 3.

4. 4. Substitution Property