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