On a piece of paper, use a protractor to construct △ABC with m∠A=30° , m∠B=60° , and m∠C=90° . Which statements about the triangles are true? Select each correct answer. A. BC&g…

Question

On a piece of paper, use a protractor to construct △ABC with m∠A=30° , m∠B=60° , and m∠C=90° .

Which statements about the triangles are true?

Select each correct answer.

A. BC>AB

B. BC>AC

C. BC<AC



D. BC<AB

Answer 1

In a triangle with angles of 30°, 60°, and 90°, the hypotenuse is the longest side. Therefore, the side opposite the right angle (AC) is longer than the other two sides, making statements BC < AC and BC < AB true.

Step-by-step explanation:

To answer the question about constructing △ABC and determining which statements about the triangle's sides are true, first, let's consider the information provided:

• m∠A = 30°
• m∠B = 60°
• m∠C = 90°

Since angle C is 90°, △ABC is a right-angled triangle. In any right-angled triangle, the hypotenuse is the longest side. Therefore, side AC, which is opposite the right angle, is the hypotenuse and the longest side.

Given this, we can answer the statements:

1. BC > AB is false because AB is opposite the 60° angle and BC is opposite the 30° angle, which means AB is longer than BC.
2. BC > AC is false because AC, as the hypotenuse, is the longest side in the triangle.
3. BC < AC is true because AC is the hypotenuse and thus is longer than BC.
4. BC < AB is true because AB is opposite the larger angle (60°) compared to BC, which is opposite the smaller angle (30°).

Therefore, the correct statements about the sides of △ABC are Statements C and D: BC < AC and BC < AB.

Answer 2

Statements C and D are true