Similarity and Proportions


Problem 1.

If with scale-factor 2/3, and XZ = 10, find AC. Also, if , what can you infer?

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 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 and 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 . 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.