Looking at the right triangle, choose THREE statements that are true.

Question

A right-angled triangle ABC is shown. 

The side AC is 8.  The side AB is 10. The angle BAC is 53.13°.  The angle ACB is 90°. The side BC is labeled 'a' and has a value of 8, the side AC is labeled 'c' and has a value of 10, and the side AB is labeled hypotenuse. The right angle is at vertex C. The vertices are labeled A, B, and C.

(3 points)
Responses

Right triangles have side lengths that always follow a2+b2=c2Right triangles have side lengths that always follow A squared plus b squared is equal to c squared

Right triangles have interior angles that are all acute angles.
Right triangles have interior angles that are all acute angles.

Right triangles have the pattern that the sum of the two shorter sides = the longest side.
Right triangles have the pattern that the sum of the two shorter sides = the longest side.

Right triangles have interior angles that add to equal 180 degrees.
Right triangles have interior angles that add to equal 180 degrees.

Right triangles have side lengths that are always rational numbers.
Right triangles have side lengths that are always rational numbers.

Right triangles must have the side across from the 90 degree angle as the longest side.

Answer 1

Based on the information provided, the following three statements about right triangles are true:

1. Right triangles have side lengths that always follow \(a^2 + b^2 = c^2\). (This is the Pythagorean theorem and is fundamental to all right triangles.)

2. Right triangles have interior angles that add to equal 180 degrees. (This is a property of all triangles, including right triangles.)

3. Right triangles must have the side across from the 90 degree angle as the longest side. (In a right triangle, the hypotenuse, which is opposite the right angle, is always the longest side.)

The other statements are false:

• Right triangles do not have all acute angles (one angle is a right angle).
• The sum of the two shorter sides does not equal the longest side; they follow the Pythagorean theorem instead.
• Side lengths do not have to be rational numbers; they can be any real numbers.