Lines and Angles

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Lines and Parts

Points and Lines Point and line are undefined ideas of Euclidean Geometry. Points have position; lines are infinite in both directions; segments and rays are parts of lines, the first being definite and the second extending infinitely from a single point.
An angle is formed by two rays.
Sun's Rays
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Angles Classification

Types of Angles
An angle is measured in degrees which represents the amount of rotation between the rays. A full rotation is 360∘. It takes the earth about 360 days to make one trip around the sun.

Vertical Angles

Vertical Angles When two lines intersect, four angles are formed. The opposite angles are called "vertical angles" and VERTICAL ANGLES ARE EQUAL. If two angles "sit" on a straight line they are called a "linear pair" and their sum is 180∘. The sum of all the angles around a point is 360∘.

Perpendicular Lines

Perpendicular Lines When two lines intersect in right angles, they are called "perpendicular lines." Notice that the vertical angles are 90∘ and still equal and all the pairs sitting on a line add to 180∘.

Self Quiz

1. Classify the angle.
Right Angle
2. If ∠a is 60∘, what is the measure of ∠b?
Supplementary Angles
3. What is the sum of ∠a+∠b+∠c+∠d+∠e?
Five Angles Sitting on a Line


1. right angle
2. 120∘
3. 360∘