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Lesson 4.2 The Case of the Missing Diagram

Cue dramatic music……. Lost Diagram! Last seen with 3 “Givens” and a “Prove” Often hangs out with triangles and circles If found please call: 1-800-I-Miss-My-Proof 1 Free HW Stamp as Reward!. Lesson 4.2 The Case of the Missing Diagram. Learning Goal:

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Lesson 4.2 The Case of the Missing Diagram

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  1. Cue dramatic music…… Lost Diagram! Last seen with 3 “Givens” and a “Prove” Often hangs out with triangles and circles If found please call: 1-800-I-Miss-My-Proof 1 Free HW Stamp as Reward! Lesson 4.2 The Caseof the Missing Diagram Learning Goal: After studying this lesson you will be able to organize the information in, and draw diagrams for, proofs presented in statements.

  2. What no picture????? Right! It will be important for you to “set up” the problem…that is, draw a diagram that accurately represents the problem and express the given information and the conclusion you must reach in terms of the diagram.

  3. Set up a proof of the following statement Example 1: “If two altitudes of a triangle are congruent, then the triangle is isosceles” The hypothesis part of the conditional statement tells us the given information. The conclusion part of the conditional statement is what we are to prove.

  4. Example 1 continued: “If two altitudes of a triangle are congruent, then the triangle is isosceles” We need some steps! Step 1: Draw a diagram and label it. Step 2: Write out the given information and what you need to prove.

  5. A E B C D Example 1 continued: “If two altitudes of a triangle are congruent, then the triangle is isosceles” Given: Prove:

  6. Your Turn… Set up a proof of the following statement Example 2: “The medians of a triangle are congruent if the triangle is equilateral.”

  7. Set up and do a proof of the following statement Example 3: “The altitude to the base of an isosceles triangle bisects the vertex angle.” Is it necessary to identify the base in the given information? How about the vertex angle? Why?

  8. Class Work Break up into six groups of 3 or 4…I will be coming around for you to draw a homework problem that your group will be responsible for. You are to draw a diagram, state the givens and prove, and complete the proof! Please write legibly as you will be presenting to the class!

  9. Homework: Make sure the problem your group was responsible for is completed (proof and all!) and be ready to present in class tomorrow!

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