Section 1
Similarity in Right Triangles
Simplify.$$\sqrt{12}$$
Simplify.$$\sqrt{72}$$
Simplify.$$\sqrt{45}$$
Simplify.$$\sqrt{75}$$
Simplify.$$\sqrt{800}$$
Simplify.$$\sqrt{54}$$
Simplify.$$9 \sqrt{40}$$
Simplify.$$4 \sqrt{28}$$
Simplify.$$\sqrt{30} \cdot \sqrt{6}$$
Simplify.$$\sqrt{5} \cdot \sqrt{35}$$
Simplify.$$\sqrt{\frac{3}{7}}$$
Simplify.$$\sqrt{\frac{9}{5}}$$
Simplify.$$\frac{18}{\sqrt{3}}$$
Simplify.$$\frac{24}{3 \sqrt{2}}$$
Simplify.$$\frac{\sqrt{15}}{3 \sqrt{45}}$$
Find the geometric mean between the two numbers.2 and 18
Find the geometric mean between the two numbers.3 and 27
Find the geometric mean between the two numbers.49 and 25
Find the geometric mean between the two numbers.1 and 1000
Find the geometric mean between the two numbers.16 and 24
Find the geometric mean between the two numbers.22 and 55
Refer to the figure at the right.(FIGURE CAN'T COPY)If $L M=4$ and $M K=8 .$ find $J M$
Refer to the figure at the right.(FIGURE CAN'T COPY)If $L M=6$ and $J M=4,$ find $M K$
Refer to the figure at the right.(FIGURE CAN'T COPY)If $J M=3$ and $M K=6,$ find $L M$
Refer to the figure at the right.(FIGURE CAN'T COPY)If $J M=4$ and $J K=9,$ find $L K$
Refer to the figure at the right.(FIGURE CAN'T COPY)If $J M=3$ and $M K=9,$ find $L J$
Refer to the figure at the right.(FIGURE CAN'T COPY)If $J M=3$ and $J L=6,$ find $M K$
Refer to the figure at the right.(FIGURE CAN'T COPY)If $J L=9$ and $J M=6 .$ find $M K$
Refer to the figure at the right.(FIGURE CAN'T COPY)If $L K=3 \sqrt{6}$ and $M K=6,$ find $J M$
Refer to the figure at the right.(FIGURE CAN'T COPY)If $L K=7$ and $M K=6,$ find $J M$
Find the values of $x, y,$ and $z$.(DIAGRAM CAN'T COPY)
Prove Theorem $8-1$
a. Refer to the figure at the right, and use Corollary 2 to complete:$$a^{2}=\underline{?} \text { and } b^{2}=\underline{?}$$b. Add the equations in part (a), factor the sum on the right, and show that $a^{2}+b^{2}=c^{2}$(DIAGRAM CAN'T COPY)
Prove: In a right triangle. the product of the hypotenuse and the length of the altitude drawn to the hypotenuse equals the product of the two legs.
Given: $P Q R S$ is a rectangle; $P S$ is the geometric mean between $S T$ and $T R$ Prove: $\angle P T Q$ is a right angle.(FIGURE CAN'T COPY)
Given: $P Q R S$ is a rectangle; $\angle A$ is a right angle. Prove: $B S \cdot R C=P S \cdot Q R=(P S)^{2}$(FIGURE CAN'T COPY)
The arithmetic mean between two numbers $r$ and $s$ is defined to be $\frac{r+s}{2}$a. $\overline{C M}$ is the median and $\overline{C H}$ is the altitude to the hypotenuse of right $\triangle A B C .$ Show that $C M$ is the arithmetic mean between $A H$ and $B H,$ and that $C H$ is the geometric mean between $A H$ and $B H .$ Then use the diagram to show that the arithmetic mean is greater than the geometric mean.b. Show algebraically that the arithmetic mean between two different numbers$r$ and $s$ is greater than the geometric mean. (Hint: The geometric mean is $\sqrt{r s} .$ Work backward from $\frac{r+s}{2}>\sqrt{r s}$ to $(r-s)^{2}>0$ and then reverse the steps.)(FIGURE CAN'T COPY)