Question

find one counterexample to show that the following conjecture is false. \\( \triangle abc \\) is a right triangle, so \\( \angle a \\) measures \\( 90^\circ \\). choose the correct answer below \\( \bigcirc \\)a. image of triangle with right angle at a \\( \bigcirc \\)b. image of triangle without right angle \\( \bigcirc \\)c. image of triangle with right angle at b \\( \bigcirc \\)d. image of triangle without right angle

Explanation:

Step1: Understand the Conjecture

The conjecture is: If \( \triangle ABC \) is a right triangle, then \( \angle A \) measures \( 90^\circ \). A counterexample must be a right triangle where \( \angle A \) is not \( 90^\circ \).

Step2: Analyze Each Option

• Option A: The right angle is at \( X \) (assuming \( X \) is \( A \)? Wait, no, the label is \( X \), \( B \), \( C \). Wait, maybe a typo, but looking at Option C: Triangle with right angle at \( B \). So \( \triangle ABC \) is right-angled at \( B \), so \( \angle B = 90^\circ \), hence \( \angle A

eq 90^\circ \), which is a counterexample.

• Option B: Not a right triangle (no right angle symbol), so not a counterexample.
• Option C: Right angle at \( B \), so \( \angle B = 90^\circ \), so \( \angle A \) is not \( 90^\circ \), and it's a right triangle. This is a counterexample.
• Option D: Not a right triangle (no right angle symbol), so not a counterexample.

Answer:

C. The triangle with right angle at \( B \) (the third option, labeled C)