Question

Given: (triangle ABC) with (m∠ ABC = 90^∘). What is the missing statement in the proof?

a) (BC) is the hypotenuse.
b) (AB) is the hypotenuse.
c) (AC) is the hypotenuse.
d) (m∠ ACB = 90^∘)

Answer 1

Side (BC) is the hypotenuse of the right triangle ABC, opposite angle ABC which is 90 degrees, in accordance with the options provided and the Pythagorean theorem.

Step-by-step explanation:

The student's question was: Given: (triangle ABC) with (m∠ ABC = 90^°). What is the missing statement in the proof?

The options provided are:

• (BC) is the hypotenuse.
• (AB) is the hypotenuse.
• (AC) is the hypotenuse.
• (m∠ ACB = 90^°)

The hypotenuse is the longest side of a right triangle, which is opposite the right angle. Since angle ABC is 90 degrees, side (BC) must be the hypotenuse of the triangle. Therefore, the correct missing statement in the proof is option (a): (BC) is the hypotenuse.

Using the Pythagorean theorem, which states that a² + b² = c², with c being the length of the hypotenuse and a and b being the lengths of the other two sides, it's clear that in a right-angled triangle like triangle ABC, BC being opposite the right angle must be c, the hypotenuse.