Write the first step of an indirect proof of the given statement.

18. If a number n ends in 5, then it is not divisible by 2.
19. If point X is on the perpendicular bisector of A B ¯ , eh b bar , comma  then X B ¯ ≅ X A ¯ . x b bar , approximately equal to . x eh bar , .
20. If a transversal intersects two parallel lines, then alternate exterior angles are congruent.
21. Reasoning Identify the two statements that contradict each other.
    1. The orthocenter of Δ J R K cap delta j r k  is on the triangle.
    2. The centroid of Δ J R K cap delta j r k  is inside the triangle.
    3. Δ J R K cap delta j r k  is an obtuse triangle.

Write an indirect proof.

22. Proof Use the figure below.

    

    Given: Δ A B C cap delta eh b c  with B C > A C b c greater than eh c

    Prove: ∠ A ≇ ∠ B angle eh neither approximately nor actually equal to angle b

23. Proof

    Given: Δ X Y Z cap delta x y z  is isosceles.

    Prove: Neither base angle is a right angle.

Writing For Exercises 24 and 25, write a convincing argument that uses indirect reasoning.

24. Chemistry Ice is forming on the sidewalk in front of Toni's house. Show that the temperature of the sidewalk surface must be 32 ° F 32 degrees cap f  or lower.
25. Show that an obtuse triangle cannot contain a right angle.
26. Error Analysis Your friend wants to prove indirectly that Δ A B C cap delta eh b c  is equilateral. For a first step, he writes, “Assume temporarily that Δ A B C cap delta eh b c  is scalene.” What is wrong with your friend's statement? How can he correct himself?

27. Literature In Arthur Conan Doyle's story “The Sign of the Four,” Sherlock Holmes talks to his friend Watson about how a culprit enters a room that has only four entrances: a door, a window, a chimney, and a hole in the roof.

    
    Image Long Description

    How did the culprit enter the room? Explain.

28. Open-Ended Describe a real-life situation in which you used an indirect argument to convince someone of your point of view. Outline your argument.

Table of Contents