Lesson 5 Getting Your Share of the Pie Develop Understanding

Ready

1.

Prove that $△ A B C \sim △ D E F$ .

2.

Use the given information and the diagram to find $B D$ . Justify each step of your work.

Given: $\overset{―}{A B} ⊥ \overset{―}{A C}$ and $\overset{―}{D E} ⊥ \overset{―}{A C}$ .

3.

Given: $\overset{―}{D E} ∥ \overset{―}{A C}$

Prove $△ A B C \sim △ D B E$

4.

Given: $\overset{―}{E F} ∥ \overset{―}{D G}$

Prove $△ D H G \sim △ F H E$

Set

A lever is a simple machine consisting of a bar that pivots on a fixed support, or fulcrum. It is used for making it possible to lift a heavy object.

$d_{1} \cdot input = d_{2} \cdot weight$

Use the information about a lever to solve the following problems.

5.

A child who weighs $80 lbs$ is sitting on a teeter-totter $5 ft$ from the fulcrum. Where should a child that weighs $60 lbs$ sit in order to balance the teeter-totter?

6.

A landscaper needs to lift a large rock that weighs $150 lbs$ . What is the minimum force he needs to apply if his crowbar has a $6 -inch$ length between the rock and the pivot point and $3 ft$ between the pivot and where he plans to apply his force?

7.

The lid of a can of paint is wedged into the can and surrounded by dried paint. A painter is using a screwdriver to lift it. The friction between the lid and the can, including the weight of the lid and the dried paint, will require $275 lbs$ of force to overcome it. The fulcrum is $11 inches$ away from where the painter is applying a downward force to pry open the lid, and the lid is $0.25 inches$ from the fulcrum. What minimum force will he need to apply to the screwdriver to open the can?

8.

Explain how this formula $d_{1} \cdot w e i g h t_{1} = d_{2} \cdot w e i g h t_{2}$ represents an inverse variation relationship.

9.

Show that if $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ satisfy the equation $x y = k$ , then $\frac{x_{1}}{x_{2}} = \frac{y_{2}}{y_{1}}$ .

Go

Solve each equation for all solutions.

10.

$x^{2} = 8 x + 33$

11.

$x^{2} + 19 x = - x - 75$

12.

$x^{2} = 144$

13.

$x^{2} - 121 = 0$

14.

$4 x^{2} + 8 x = - 1$

15.

$2 x^{2} = x + 2$