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Angle • Two rays with the same endpoint. • The rays are the sides of the angle . • The common endpoint of the 2 rays is the vertex of the angle. Name the sides and vertex of this angle:. Name the sides and vertex of this angle:.
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• The rays are the sides of the angle. • The common endpoint of the 2 rays is the vertex of the angle.
We sometimes refer to the interior and exterior of an angle.
What points lie on the interior? on the exterior? on the angle?
• named with 1 letter, the letter must be the vertex• named with 3 letters, the middle letter is the vertex, and the others are 1 point on each ray
Give as many names as you can for these angles.DEFFEDE
Give as many names as you can for these angles.TUVVUTU
We sometimes also name angles with numbers, particularly when there are several angles in the same picture.5 is atthe bottomleft.
The measure of an angle refers to how wide the angle opens, NOT how long the sides are (because they go on forever) or which way it points.
There aremany waysto measure angles.The oldest and most common unit of measurement is the degree.
• Acute• less than 90o• Right •exactly 90o •We often use a box to show an angle is a right angle.
• Obtuse • between 90o and 180o• Straight •exactly 180o •same as a line
Various types of protractors have been used for thousands of years, mostly in navigation and construction.
In modern practical applications, angles are measured by sighting laser beams.
We refer to the measure of an angle with notation that uses the letter “m”.mACD = 138mB = 80
IMPORTANT:We don’t normally use protractors much in geometry. This is because pictures are intended to give the idea of what’s going on, but they may not necessarily be accurate.
Congruent AnglesAngles are congruent if and only if they have the same measure.R Q
In drawings we show angles are congruent by marking the same arcs of a circle inside the angles.
mADC = 50Find xFind m BDCm BDC = 2x + 192 8 + 19 = 16 + 19 = 35o
Remember … Angle, side vertex, interior, exterior Naming angles Measuring angles, protractor, degree Acute, obtuse, right, straight Congruent angles