4.2 The Case of the Missing Diagram

1. 4.2 The Caseof the Missing Diagram Objective: After studying this lesson you will be able to organize the information in, and draw diagrams for, problems presented in words.

2. What no picture????? Right! It will be important for you to “set up” the problem—that is, to draw a diagram that accurately represents the problem and to 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. A E B C D Example 1 con’t.: “If two altitudes of a triangle are congruent, then the triangle is isosceles” Step 1: Draw a diagram and label it. Step 2: Write out the given information and what you are to prove. Given: Prove:

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

6. Set up 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?

7. Set up a proof of the following statement Example 4: “If two angles of one triangle are congruent to two angles of another triangle, the remaining pair of angles are also congruent.” Why should we not draw an isosceles or equilateral triangle? Do the triangles need to be the same size?

8. Set up AND supply the proof of the statement Example 5: “The altitude to a side of a scalene triangle forms two congruent angles with that side of the triangle.” Given: Prove: Statements Reasons 1. 2. 3. 4. 5. 1. 2. 3. 4. 5.

9. Summary: How do you set up the proof of a problem that is presented in words? Homework: worksheet