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

## Vocabulary[edit]

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 30^{0}, 60^{0}, and 90^{0}, and triangle DEF has side lengths 2, 2*square root of 3, and 4, and angles of 30^{0}, 60^{0}, and 90^{0}, then triangles ABC and DEF are similar, because their corresponding angles are equal, and their corresponding sides are proportional to each other.)

## Lesson[edit]

## Example Problems[edit]

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=60^{0}.

Since corresponding angles are congruent in similar triangles,

angle C=angle F=60^{0}