Video narration
What happens when a line parallel to a triangle's base crosses its two sides? With a ruler, draw triangle ABC. Put D on AB and E on AC, then draw DE parallel to BC. This cut does not make the pieces equal; it makes the corresponding ratios equal. This is the Basic Proportionality Theorem: AD/DB = AE/EC. To check it, compare the two segment ratios. The parallel line divides both sides in the same ratio.