Mai is playing a game with a class of second graders. Mai knows that she is exactly 120 inches from the mirror on the floor. She has students stand so that she can just see the top of their heads and then guesses their heights. The students are amazed!

Diagram of 2 stick figures. For each, diagonal line drawn from head, horizontal line drawn from feet, creating right triangle. For left figure: Height labeled 65 inches, distance from feet to vertex labeled 120 inches. For right figure, height labeled h, distanced from feet to vertex labeled 72 inches.

How is Mai so accurate? What is the height, \(h\), of the student? 

In right triangle \(ABC\), angle \(C\) is a right angle, \(AB=17\), and \(BC=15\). What is the length of \(AC\)?

Fill in the blanks to complete the proof of the Pythagorean Theorem:

\(\frac{a}{x} = \frac{c}{a} \) can be rewritten as \(\underline{\hspace{.5in}1\hspace{.5in}}\) and \(\frac{b}{y}=\frac{c}{b}\) can be written as \(\underline{\hspace{.5in}2\hspace{.5in}}\). So, \(a^2+b^2=\)\(\underline{\hspace{.5in}3\hspace{.5in}}\). By factoring, \(a^2+b^2=\) \(\underline{\hspace{.5in}4\hspace{.5in}}\). We know that \(x+y=\)\(\underline{\hspace{.5in}5\hspace{.5in}}\). So, \(a^2+b^2=\)\(\underline{\hspace{.5in}6\hspace{.5in}}\).

Match each vocabulary term with its definition.

Clare and Diego are discussing the quadrilaterals. Clare thinks the quadrilaterals are similar because the side lengths are proportional. Diego thinks they need more information to know for sure if they are similar. Do you agree with either of them? Explain your reasoning.