Question

In triangle PQR m angle P=60°, and m angle Q=30°, and m angle R=90°. Which of the following statements about triangle PQR are true? Check all that apply.

Answer 1

In triangle PQR, statement 1 and 3 are true. Statement 2 and 4 are false.

Step-by-step explanation:

In triangle PQR, the measure of angle P is 60°, angle Q is 30°, and angle R is 90°. To determine which statements about triangle PQR are true, we can use the properties of triangles:

1. The sum of the angles of a triangle is always 180°. Therefore, 60° + 30° + 90° = 180°, so this statement is true.
2. By the angle sum property of triangles, the longest side of a triangle is opposite the largest angle. In this case, angle R is the largest angle, so QR is the longest side. Therefore, statement 2 is false.
3. By the angle sum property of triangles, the smallest side of a triangle is opposite the smallest angle. In this case, angle Q is the smallest angle, so PQ is the shortest side. Therefore, statement 3 is true.
4. The side opposite a right angle in a right triangle is called the hypotenuse. In this case, angle R is a right angle, so QR is the hypotenuse. Therefore, statement 4 is true.

Answer 2

Answer: A, C, and F

Step-by-step explanation: