Similarity and Proportions

Author:: Adam

Problem 1.

with scale-factor 2/3, and XZ = 10, find AC. Also, if

, what can you infer?

Problem 2.

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.

what must be true about the triangle?

Problem 4.

In the diagram below

. Show that the scale factor is

Problem 5.

the point X is the midpoint of

and Y is the midpoint of

. Prove that

and find the scale-factor.

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

. If AA''=10 and AB=15 and A''B''=5, then determine A''C.

Problem 9.

Suppose a/b = c/d. Simplify the expression

. 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 a/b = c/d the expression

simplifies back down to

. Can you prove that this is always true?

Problem 10.

In the figure below, suppose

is equilateral. Solve for x.

Problem 11.

In the figure below, it is given that