Lesson 06: Finding Side Lengths of Triangles | Unit 8: Pythagorean Theorem and Irrational Numbers

Open Ended

Here is a diagram of an acute triangle and three squares. An acute triangle with squares along each side of the triangle. Each square has sides equal to the length of the side of the triangle it touches. The square on the bottom is touching the shortest side and is labeled 9. The square on the top right is touching the next longest side and is labeled 17. The square on the top left is touching the longest side and is unlabeled. Priya says the area of the large unmarked square is 26 square units because $$9+17=26$$ . Do you agree? Explain your reasoning.

Multiple Select

Select **all** the equations that represent the relationship between $$m$$ , $$p$$ , and $$z$$ in the right triangle.

• $$m^2=z^2+p^2$$

• $$m^2=p^2+z^2$$

• $$p^2+z^2=m^2$$

• $$p^2+m^2=z^2$$

• $$m^2+p^2=z^2$$

Multiple Choice

The lengths of the three sides (in units) are given for a right triangle. For the triangle with sides 10, 6, and 8, which equation expresses the relationship between the lengths of the three sides?

• 10^2 = 6^2 + 8^2
• 6^2 = 10^2 + 8^2
• 8^2 = 6^2 + 10^2
• 10^2 = 10^2 + 6^2

Multiple Choice

The lengths of the three sides (in units) are given for a right triangle. For the triangle with sides $$\sqrt5, \sqrt3, \sqrt8$$ , which equation expresses the relationship between the lengths of the three sides?

• $\sqrt{5}^2 = \sqrt{3}^2 + \sqrt{8}^2$
• $\sqrt{3}^2 = \sqrt{5}^2 + \sqrt{8}^2$
• $\sqrt{8}^2 = \sqrt{5}^2 - \sqrt{3}^2$
• \sqrt{8}^2 = \sqrt{5}^2 + \sqrt{3}^2

Multiple Choice

The lengths of the three sides (in units) are given for a right triangle. For the triangle with sides 5, $$\sqrt5, \sqrt{30}$$ , which equation expresses the relationship between the lengths of the three sides?

• 5^2 = (\sqrt{30})^2 + (\sqrt{5})^2
• (\sqrt{5})^2 = 5^2 + (\sqrt{30})^2
• (\sqrt{30})^2 = (\sqrt{5})^2 + 5^2
• 5^2 = (\sqrt{5})^2 + (\sqrt{30})^2

Multiple Choice

The lengths of the three sides (in units) are given for a right triangle. For the triangle with sides 1, $$\sqrt{37}$$ , and 6, which equation expresses the relationship between the lengths of the three sides?

• 6^2 = (sqrt{37})^2 - 1^2
• (sqrt{37})^2 = 1^2 + 6^2
• 6^2 = 1^2 + (sqrt{37})^2
• 1^2 = 6^2 + (sqrt{37})^2

Multiple Choice

The lengths of the three sides (in units) are given for a right triangle. For the triangle with sides 3, $$\sqrt{2}$$ , and $$\sqrt7$$ , which equation expresses the relationship between the lengths of the three sides?

• $\sqrt{2}^2 = 3^2 + (\sqrt{7})^2$
• $3^2 = \sqrt{7}^2 + (\sqrt{2})^2$
• $\sqrt{7}^2 = 3^2 - (\sqrt{2})^2$
• \sqrt{7}^2 = 3^2 + (\sqrt{2})^2

Multiple Choice

Which of the following orders the expressions from least to greatest? $$25\div 10$$ , $$250,\!000 \div 1,\!000$$ , $$2.5 \div 1,\!000$$ , $$0.025\div 1$$

• 25 ÷ 1,000, 2.5 ÷ 10, 250,000 ÷ 1
• 0.025 ÷ 10, 2.5 ÷ 1,000, 250,000 ÷ 10
• 2.5 ÷ 1,000, 0.025 ÷ 1, 25 ÷ 10, 250,000 ÷ 1,000
• 250,000 ÷ 1,000, 0.025 ÷ 1,000, 25 ÷ 1,000

Multiple Choice

For which triangle, does the Pythagorean Theorem express the relationship between the lengths of its three sides?

• A

• B

• C

• D

Multiple Choice

Select all the equations that represent the relationship between $$m$$ , $$p$$ , and $$z$$ in the right triangle shown in the image.

• $$m^2+p^2-z^2=0$$

• $$m^2+z^2-p^2=0$$

• $$m^2-z^2=p^2$$

• $$z^2-p^2=m^2$$

• $$m^2-p^2=z^2$$