A Mathematician's Lament by Paul Lockhart

A Mathematician's Lament by Paul Lockhart

Author:Paul Lockhart [Lockhart, Paul]
Language: eng
Format: epub
ISBN: 9781934137338
Publisher: Bellevue Literary Press
Published: 2010-07-06T04:00:00+00:00


THEOREM 9.5.

Let Δ ABC be inscribed in a semicircle

with diameter .

Then ∠ABC is a right angle.

Proof:

STATEMENTREASON

1. Draw radius OB. Then OB = OC A 1. Given

2. m∠OBC = m∠BCA m∠OBA = m∠BAC 2. Isosceles Triangle Theorem

3. m∠ABC = m∠OBA + m∠OBC 3. Angle Sum Postulate

4. m∠ABC + m∠BCA + m∠BAC = 180 4. The sum of the angles of a triangle is 180

5. m∠ABC + m∠OBC + m∠OBA = 180 5. Substitution (line 2)

6. 2 m∠ABC = 180 6. Substitution (line 3)

7. m∠ABC 90 7. Division Property of Equality

8. ∠ABC is a right angle 8. Definition of Right Angle



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