Triangle Congruence Calculator

The formula

similar triangles have equal angles and a constant side ratio

Lengths scale, areas square

If two triangles are similar with scale factor k, every length scales by k but the area scales by k². Double a triangle and it holds four times the area. This is the single most commonly missed step in similarity problems.

What always holds

• The three angles add to 180°, without exception.
• Any two sides must add to more than the third — the triangle inequality. Sides of 4, 5 and 12 cannot close.
• The longest side always faces the largest angle.
• Area = ½ × base × height for any triangle, with the height measured perpendicular to that base.

Which formula to reach for

With three sides, use Heron’s formula. With a base and its height, use ½bh. With two sides and the angle between them, use ½ab·sin C. With a right angle, the two legs are already base and height, so the area is just half their product.