# Basic Algebra/Proportions and Proportional Reasoning/Solving Similar Triangles using Proportions

## Vocabulary

Proportions - Proportions are equations resulting from two or more ratios. (Ex. 2/3 = 4/x)

Similar triangles - have equal corresponding angles and proportional corresponding sides (Ex. If triangle ABC has side lengths 1, square root of 3, and 2, and angles of 300, 600, and 900, and triangle DEF has side lengths 2, 2*square root of 3, and 4, and angles of 300, 600, and 900, then triangles ABC and DEF are similar, because their corresponding angles are equal, and their corresponding sides are proportional to each other.)

## Example Problems

Proportions:

2/3 = 4/x
Cross-multiply: 2x = 12
Divide both sides by 2: x = 6

Similar Triangles:
If Triangles ABC and DEF are similar:

Find DE if AB=3, BC=4, EF=8.
Since AB/DE = BC/EF,
3/DE = 4/8
Solving the proportion: DE=6
Find angle C when angle F=600.
Since corresponding angles are congruent in similar triangles,
angle C=angle F=600