ANGLES.

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Presentation transcript:

ANGLES

You will learn to classify angles as acute, obtuse, right, or straight.

What is an angle? Two rays that share the same endpoint form an angle. The point where the rays intersect is called the vertex of the angle. The two rays are called the sides of the angle.

Here are some examples of angles.

We can identify an angle by using a point on each ray and the vertex We can identify an angle by using a point on each ray and the vertex. The angle below may be identified as angle ABC or as angle CBA; you may also see this written as ABC or as CBA. The vertex point is always in the middle.

Protractor A device used to measure angles.

Angle Measurements We measure the size of an angle using degrees. Here are some examples of angles and their degree measurements.

Acute Angles An acute angle is an angle measuring between 0 and 90 degrees. The following angles are all acute angles.

Obtuse Angles An obtuse angle is an angle measuring between 90 and 180 degrees. The following angles are all obtuse.

Right Angles A right angle is an angle measuring 90 degrees. The following angles are both right angles.

Straight Angle A straight angle is 180 degrees.

Example: Complementary Angles Two angles are called complementary angles if the sum of their degree measurements equals 90 degrees. Example: These two angles are complementary.

These two angles can be "pasted" together to form a right angle!

Complementary angles add up to 90º. 30º 40º 50º 60º Adjacent and Complementary Angles Complementary Angles but not Adjacent

Two angles are called supplementary angles if the sum of their degree measurements equals 180 degrees. Example: These two angles are supplementary.

Supplementary angles add up to 180º. 40º 120º 60º 140º Adjacent and Supplementary Angles Supplementary Angles but not Adjacent

These two angles can be "pasted" together to form a straight line!

Vertical Angles For any two lines that meet, such as in the diagram below, angle AEB and angle DEC are called vertical angles. Angle BEC and angle AED are also vertical angles. Vertical angles have the same degree measurement. 110 70 70 110

Adjacent, Vertical, Angles

Vertical Angles Find the missing angle. You do not have a protractor. Use the clues in the pictures. X=58 x 58

Adjacent angles are “side by side” and share a common ray. 15º 45º

These are examples of adjacent angles. 45º 80º 35º 55º 130º 50º 85º 20º

These angles are NOT adjacent. 100º 50º 35º 35º 55º 45º

When 2 lines intersect, they make vertical angles. 75º 105º 105º 75º

Vertical angles are opposite one another. 75º 105º 105º 75º

Vertical angles are opposite one another. 75º 105º 105º 75º

Vertical angles are congruent (equal). 150º 30º 150º 30º

Final Drawing B C 68 60 52 A G D 60 52 68 F E