# Triangles

Words of “Wiz-dom”-There are three basic rules about triangles that you need to remember. First, don’t forget the “Wizard’s Theorem” which applies to all triangles not just right triangles. The sum of the lengths of any two sides of a triangle is greater than the length of the third side and the length of the third side is greater than the difference of the other two sides. This pair of rules can be written as the following:

### SUM > 3rd side > DIFFERENCE

Second, the length of the sides of a triangle are in proportion to the angles that define (are opposite) them. That is, the longest (largest) side is opposite the largest angle and the shortest (smallest) side is opposite the smallest angle.

Third, the most common rule about triangles that you need to remember is the angles of a triangle add up to 180o.

Let’s do two quick refresher exercises. If angle c is 80 degrees and d is 40:

How many degrees is angle a? Answer #1

How many degrees is angle b? Answer #2

What is the longest side? Answer #3

What is the shortest side? Answer #4

What is true about the length of NO when compared to the sum and differences of the lengths of OP and NP? Answer #5 Remember this diagram is NOT drawn to scale.

What is the range of possible lengths of LM? Answer #6

Which angle is larger L or M? Answer #7

Which angle is larger O or M? Answer #8

Words of “Wiz-dom”-Remember middle school? About then you were taught that the area of a triangle is 1/2 the length of the base times the height of the triangle. It is expressed by the following formula: More words of “Wiz-dom” on area of a triangle

Here’s another refresher exercise you need to be able to do! Draw a line that represents the height of the triangle JKL, using JL as the base. Let’s try a quick refresher exercise. In the triangle above, the area is 42 and the base is 7.

What is the height?

Which angle is smallest?

### Sample Questions Note: Figure not drawn to scale.

1.  AD bisects angle BAC and CD bisects angle BCA. What is the size of angle x?

A. 120
B. 100
C. 90
D. 80
E. 40 2.  If the ratio of x:y is 7:5 and the area of triangle LMN is 60, what is the area of triangle KLN?

A. 84
B. 76
C. 52
D. 42
E. 35