Tip #26 to Get a Top ACT Math Score
I shall call him … "Mini-Me."
Dr. Evil, Austin Powers: The Spy Who Shagged Me (New Line Cinema, 1999)
Similar triangles are two triangles where one is a shrinky version of the other, like Dr. Evil and Mini-Me. Since one is a shrunken version of the other, all sides are proportional, shortest to shortest and longest to longest. The ACT loves similar triangles.
Let's have a look at this question:
Solution: Here's your chance to see if you really learned Skill 25. We have to determine the measures of sides of triangle PQR shown above. Fill in the sides of special right triangle ΔPQR: 3, , 6. Once you have the lengths of the sides of ΔPQR, we can determine the lengths of ΔMNO. Triangle MNO is "similar" to triangle PQR, which means that the sides are proportional. So the ratio of the smallest sides must equal the ratio of the longest sides. Fill in the numbers and cross-multiply to solve. (Remember Mantra #21, "When you see a proportion, cross-multiply.")
So 3x = 27 and x = 9.
Correct answer: H
- In the figure below, ΔXYZ and ΔPQR are similar triangles with the side lengths given in feet. What is the perimeter, in feet, of ΔXYZ ?
- Isosceles triangle ΔABC is similar to triangle ΔMNO. If AC = 4, AB = 5, BC = 4, and MN = 15, what is the measure of MO ?
- A person 2 meters tall casts a shadow 4 meters long. At the same time a lamppost casts a shadow 15 meters long. How many meters tall is the lamppost?
- Triangle ΔPQR is similar to triangle ΔXYZ. is 6 centimeters, is 8 centimeters, and is 14 centimeters. If the longest side of ΔXYZ is 35 centimeters, what is the perimeter, in centimeters, of ΔXYZ ?
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