Question

find one counterexample to show that the following conjecture is false. δabc is a right triangle, so ∠a measures 90°. choose the correct answer below

Explanation:

Step1: Understand the conjecture

The conjecture is that in right triangle \( \triangle ABC \), \( \angle A \) must be \( 90^\circ \). A counterexample would be a right triangle where \( \angle A \) is not \( 90^\circ \).

Step2: Analyze the options

• Option A: The triangle doesn't appear to be a right triangle (no right angle symbol), so it's not a counterexample.
• Option B: The triangle doesn't appear to be a right triangle (no right angle symbol), so it's not a counterexample.
• Option C: The right angle is at \( \angle B \) (marked with the right angle symbol), so \( \triangle ABC \) is a right triangle, but \( \angle A \) is not \( 90^\circ \). This is a counterexample to the conjecture.

Answer:

C. In \( \triangle ABC \) (option C), the right angle is at \( \angle B \), so \( \triangle ABC \) is a right triangle but \( \angle A \) does not measure \( 90^\circ \), showing the conjecture is false.