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If D lies in the interior of ∠ABC, then
m∠ABD + m∠DBC = m∠ABC. |
This concept may also be referred to as
"whole quantity" or "the whole is equal to the sum of its parts." |
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An angle bisector is a ray from the vertex of the angle into the interior of the angle forming two congruent angles (angles of equal measure).
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Remember that the word "bisect" means to cut into two equal pieces. |
Angles Forming a Straight Line |
If the non-shared sides of two, or more, adjacent angles form a straight line, the measures of the angles add up to 180º.
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m∠1 + m∠2 + m∠3 = 180º
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This is a "common sense" rule. A straight line is also a straight angle, which contains 180º. If these angles are adjacent (don't overlap), and their non-shared sides form a straight line, the angles comprise a straight angle which contains 180º. |
If two, or more, adjacent angles completely surround a point, the measures of the angles add up to 360º.
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m∠1 + m∠2 + m∠3 = 360º
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This is also a "common sense" rule. The complete revolution around a point is a circular 360º. If these angles are adjacent (don't overlap), and together they form one complete revolution, the measures of the angles will total 360º. |
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