1. Is the triangle a right triangle?
2. Is the triangle a right triangle? The figure is not drawn to scale.
3. Which lengths could represent the side lengths of a right triangle?
I. 7 comma 10 comma , square root of 132
II. 5 comma 11 comma , square root of 146
III. 6 comma 87 comma square root of 87
4.
a. Writing Decide if the triangle is a right triangle. The figure is not drawn to scale.
A. No, because 16^{2} + 18^{2} ≠ 34^{2}.
B. Yes, because 16^{2} + 18^{2} = 34^{2}.
C. No, because 16+ 18 ≠ 34.
D. Yes, because 16+ 18 = 34.
b. How can you use your results to decide if a triangle with side lengths 8, 9, and 17 is a right triangle?
5. Reasoning Is the triangle a right triangle? The figure is not drawn to scale.
A. No, because a + b ≠ c.
B. Yes, because a ^{2} + b ^{2} = c ^{2}.
C. No, because a ^{2} + b ^{2} ≠ c ^{2}.
D. Yes, because a + b = c.
6. Error Analysis Three students draw triangles with the side lengths listed below. Each student says his triangle is a right triangle.
Student 1: 24, 18, 42
Student 2: 30, 72, 78
Student 3: 12, 18, 30
a. Which students are incorrect?
b. What mistake might they have made?
7. Multiple Representations Which lengths represent the side lengths of a right triangle? Draw each triangle to verify your answer.
Triangle 1: 12, 9, 21
Triangle 2: 15, 36, 39
Triangle 3: 9, 12, 15
8. Metalworking A machine in a factory cuts out triangular sheets of metal. Which of the triangles are right triangles? Select all that apply.
9. The lengths of the sides of a triangle are 4.5, 6, and 7. Is the triangle a right triangle?