# Similarity and Proportions

- Author:
- Adam

## Problem 1.

If with scale-factor 2/3, and , what can you infer?

*XZ*= 10, find*AC*. Also, if## Problem 2.

If with scale factors 2 and 3 respectively,
a) Can we infer that
b) If so, what is the scale-factor?
c) If the perimeter of is 60, what are the perimeters of the other two triangles?

## Problem 3.

If what must be true about the triangle?

## Problem 4.

In the diagram below . Show that the scale factor is .

## Problem 5.

In the point and . Prove that and find the scale-factor.

*X*is the midpoint of*Y*is the midpoint of## Problem 6.

In the figure below, if and

*AC=BC*then find*x, y,*and*z*. Hint: Make sure you use both of the facts that I mentioned here. Second hint: Look for similar triangles that aren't the same ones you always identify in problems that look like this.## Problem 7.

Suppose and that is an altitude of the first triangle and is an altitude of the second. If

*EF=12*and*BC=4*and*AX=5*then find*DY*.## Problem 8.

In the figure below suppose and and and . If

*AA''=10*and*AB=15*and*A''B''*=5, then determine*A''C.*## Problem 9.

Suppose .
To help you think about this, take the example where 5/4 = 25/20. In that case . From this example we could guess that, whenever simplifies back down to . Can you prove that this is always true?

*a/b*=*c/d.*Simplify the expression*a/b*=*c/d*the expression## Problem 10.

In the figure below, suppose is equilateral. Solve for

*x*.## Problem 11.

In the figure below, it is given that .

*.*Prove that## Problem 12.

Suppose and are triangles. How much of the following information is the least amount necessary to decide whether the triangles are similar or not?
I.

*AB=10*and*DE=20*II.*BC=10*and*EF=20*III.*CD=10*and*FD=10*a) I only. b) I and II. c) III only. d) I, II, and III.