Proof: Problem 3 Writing an Indirect Proof
Given:
Prove:
| Think | Write |
|---|---|
| Assume temporarily the opposite of what you want to prove. | Assume temporarily that two angles of
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| Show that this assumption leads to a contradiction. | By the Converse of the Isosceles Triangle Theorem, the sides opposite
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| Conclude that the temporary assumption must be false and that what you want to prove must be true. | The assumption that two angles of
|
✓ Got It?
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Given:
Prove:
✓ Lesson Check
Do you know HOW?
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Suppose you want to write an indirect proof of the following statement. As the first step of the proof, what would you assume?
Quadrilateral ABCD has four right angles.
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Write a statement that contradicts the following statement. Draw a diagram to support your answer.
Lines a and b are parallel.
Do you UNDERSTAND?
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Error Analysis A classmate began an indirect proof as shown below. Explain and correct your classmate's error.
Practice and Problem-Solving Exercises
A Practice
See Problem 1.
Write the first step of an indirect proof of the given statement.
- It is raining outside.
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- At least one angle is obtuse.
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Table of Contents
- 6-1 The Polygon Angle-Sum Theorems
- 6-2 Properties of Parallelograms
- 6-3 Proving That a Quadrilateral Is a Parallelogram
- 6-4 Properties of Rhombuses, Rectangles, and Squares
- 6-5 Conditions for Rhombuses, Rectangles, and Squares
- 6-6 Trapezoids and Kites
- 6-7 Polygons in the Coordinate Plane
- 6-8 and 6-9 Coordinate Geometry and Coordinate Proofs