GEOMETRY

TRIANGLES Equilateral, Isosceles and Scalene There are three special names given to triangles that tell how many sides (or angles) are equal. There can be 3, 2 or no equal sides/angles: Equilateral Triangle Equilateral Triangle Three equal sides Three equal angles, always 60° Isosceles Triangle Isosceles Triangle Two equal sides Two equal angles Scalene Triangle Scalene Triangle No equal sides No equal angles What Type of Angle? Triangles can also have names that tell you what type of angle is inside: Acute Triangle Acute Triangle All angles are less than 90° Right Triangle Right Triangle Has a right angle (90°) Obtuse Triangle Obtuse Triangle Has an angle more than 90° Combining the Names Sometimes a triangle will have two names, for example: Right Isosceles Triangle Right Isosceles Triangle Has a right angle (90°), and also two equal angles Can you guess what the equal angles are? Play With It ... Try dragging the points around and make different triangles: Needs Flash Player View Larger You might also like to play with the Interactive Triangle. Perimeter The perimeter is the distance around the edge of the triangle: just add up the three sides: Needs Flash Player Area triangle b h The area is half of the base times height. "b" is the distance along the base "h" is the height (measured at right angles to the base) Area = ½ × b × h The formula works for all triangles. Note: another way of writing the formula is bh/2 Example: What is the area of this triangle? Triangle (Note: 12 is the height, not the length of the left-hand side) Height = h = 12 Base = b = 20 Area = ½ × b × h = ½ × 20 × 12 = 120 The base can be any side, Just be sure the "height" is measured at right angles to the "base": Needs Flash Player (Note: You can also calculate the area from the lengths of all three sides using Heron's Formula.) Why is the Area "Half of bh"? Imagine you "doubled" the triangle (flip it around one of the upper edges) to make a square-like shape (it would be a "parallelogram" actually), THEN the whole area would be bh (that would be for both triangles, so just one is ½ × bh), like this: triangle area By slicing the new triangle and moving the sliced part to the other side you get a simple rectangle, whose area is bh.