Angles & Triangles

Angle

An angle is a combination of “two rays” (half lines) with a common end point.
a. Common end point = vertex
b. Rays as the sides = legs or arms of the angle.
Acute angle
Less than 90o
a. An angle whose measure is less than 90o is called an acute angle.
b. Acute angles are the smallest being between 0 and 90o.
Obtuse angle
Between 90o and 180o
An angle whose measure is greater than 90o but less than 180o, is called an obtuse angle.
Right angle
An angle whose measure is exactly 90o.
Straight angle
An angle whose measure is exactly 180o i.e. a straight line
Reflex angle
An angle whose measure is greater than 180 o but less than 360o is a reflex angle.
Full angle
An angle whose measure is exactly 3600 i.e. a full circle
Allied angles
a. “Allied angle is an angle pair, which is created by trans-versal line.”
b. Allied angles are also known as:
(i) Co-interior    (ii) Adjacent interior
Explanation
a. If I draw two parallel lines cut by a transversal, then allied angles are between the parallel lines and on the same side of transversal.
b. The allied angle theorem states that allied angles are supplementary.
c. A line that meets two or more parallel lines is called a transversal line.
5. Complementary angles

a. Two angles whose sum totals 90o degree.
b. Two angles are complementary when they add up to 90o degrees.
c. They don’t have to be next to each other; just the sum total must be 90o.
Example
(i) 60o and 30o are complementary angles.
(ii) 5o and 85o are complementary angles.
6. Supplementary angles
Two angles are supplementary when they add up to 180o.
Example
(i) 60o and 120o are supplementary angles.
(ii) 93 and 87 are supplementary angles.
7. Vertical angles
Vertical angles are the angles opposite to each other when two lines cross. They are always equal.
8. Triangle
A triangle is a closed figure with three lines and three angles. These three angles always add up to 180o.
9. Right angle triangle
A triangle in which the measure of one angle equals 90o degree.
10. Isosceles triangle
An isosceles triangle has two equal sides. The angles opposite to equal sides are also equal.
11. Right isosceles triangle
A right triangle that has 2 sides and 2 angles equal.
Explanation:
a. In such a triangle, one angle is of 90o and other two are of 45o each.
b. This triangle satisfies the Pythagorean Theorem.
12. Scalene triangle
A triangle with all sides of different lengths and different angles is called a scalene triangle.
13. Acute angle triangle
A triangle in which measures of all angles are less than 90o.
14. Obtuse triangle
Obtuse triangle is the one in which the measure of one triangle is greater than 90o.
15. Equilateral triangle
A triangle having three equal sides and three equal angles of 60o is called an equilateral triangle.