Triangles — Properties, Area, Types

ACT Math · Axiom Academy

LESSON Triangles: Properties, Area, Types The four triangle facts the ACT leans on most — how to find area, how to name a triangle, which side lengths can even close, and why the base angles match. The most common formula you'll use in geometry problems. The base is any side of the triangle; the height is the perpendicular distance from that base up to the opposite vertex — not a slanted side. Watch the height drop, the triangle fill, and the numbers resolve. height = perpendicular distance to the opposite vertex A triangle has base = 10 and height = 6. Then Area = ½ × 10 × 6 = 30 square units . Triangles are named two independent ways: by their sides and by their angles . As the top vertex slides, watch the largest angle pass through acute, right, then obtuse — the same triangle, reclassified by its angles. All three sides equal, and all three angles are 60°. Two sides equal, and the two angles opposite them are equal. No sides equal, so all three angles are different. Acute: all angles < 90°. Right: one angle = 90°. Obtuse: one angle > 90°. Not every set of three lengths makes a triangle. The two shorter sides have to be able to reach across and meet above the longest side. Watch sides 3 and 4 swing down toward the base of 8 — and fall short of touching. Try it: Can you form a triangle with sides 3, 4, and 8? Check the two short sides against the long one: 3 + 4 = 7, which is not greater than 8. 3 + 4 = 7 < 8, so the short sides can't reach. No triangle.

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