Download 8.02 Sum of Measures Sketch

Sum of the Measure of the Angles of a Triangle Sketch– Method 3
m∠ABC + m∠CBD + m∠DBE = 180 ̊ because ∠ABE is a straight angle.
∠ABC ≅∠BCD because they are alternate interior angles.
∠EBD ≅∠CDB because they are alternate interior angles.
∠CBD ≅∠DBC
Therefore m∠BCD + m∠CBD + m∠CDB = 180 ̊.
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It may be necessary to break the drawing into steps so that students can
see and mark the congruent angles.
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Using this method also leads to the fact that an exterior angle (∠BDF)is
supplementary to the adjacent interior angle (∠CBD) and that the exterior
angle is congruent to ∠ABD. Its measure is equal to the sum of the other two
(remote/non-adjacent) interior angles.
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From above, ∠BDF ≅ ∠ABD and ∠ABC ≅∠BCD.
m∠BDF = m∠ABC + m∠CBD
Therefore the measure of ∠BDF (an exterior angle) is equal to the sum of the
measures of ∠BCD and ∠CBD, the remote interior angles.
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