CHARTS & TABLES Triangles
CHARTS & TABLES Triangles
Triangles
A triangle is a polygon that has three sides and three angles. The sum of the angles of
a triangle always equals 180°.
Right triangle—one 90°angle
Isosceles triangle—two sides that are equal in length
Isosceles right triangle—two sides equal in length, plus one 90°angle
Equilateral triangle—all three sides are equal in length
Scalene triangle—no two sides are equal in length
Oblique-angled triangle—no right angles
Acute triangle—all angles measure less than 90°
The anglesof a triangle are signified with capital letters A, B,and C.
The sidesof a triangle are signified with lowercase letters a, b,and c.
The sideof a triangle that is opposite the angleis signified with the same letter. For
example, the side opposite angle Ais side a.The side opposite angle Bis side b.The
side opposite angle Cis side c.
The hypotenuseof a right triangle is the side opposite the right angle. This side is
also always the longest side of a right triangle. The remaining sides are called legs.
The Pythagorean Theoremis used to determine the length of a side of a right
triangle. It states that the square of the length of the hypotenuse equals the sum of the
squared lengths of the other two sides. This is written as a^2 + b^2 = c^2.
30 °– 60°– 90°triangle: A right triangle in which one of the other angles equals 30°,
and the remaining angle equals 60°.
The lengths of the sides of a 30°– 60°– 90°triangle are:
Half the length of the hypotenuse on the side opposite the 30°angle.
This is written as a= c/2.
Half the length of the hypotenuse times √–3 on the side opposite the 60°angle.
This is written as b= c/2 ×√–3.
An isosceles right triangle:
Has angles measuring 45°– 45°– 90°.
A= B= 45°.
C= 90°.
Has two sides that are equal in length.
This is written as a= b.
The lengths of the two equal sides are half the hypotenuse times √–2.
This is written as b = c/2 ×√–2, where a= b.