Mathematics, 12.02.2021 14:00 mriffell11
Complete the proof of the Pythagorean theorem.
Given: β³ is a right triangle, with
a right angle at β .
Prove: ^2
+^2
= ^2
Statement Reason
1. β³ is a right triangle, with a right angle
at β .
1. Given
2. Draw an altitude from point C to. 2. From a point not on a line, exactly one
perpendicular can be drawn through the point to
the line.
3. β and β are right angles. 3. Definition of altitude
4. β β
β 4. All right angles are congruent.
5. β β
β 5.
6. 6. AA Similarity Postulate
7.
/x
=
/a
7.
8. ^2= 8.
9. β β
β 9.
10. β β
β 10.
11. 11. AA Similarity Postulate
Statement Reason
12. /y
=c/b
= 12.
13. ^2 = 13.
14. ^2+ ^2 = + 14.
15. 15. Distributive Property
16. + = 16.
17. ^2+b^2=c^2 17.
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Complete the proof of the Pythagorean theorem.
Given: β³ is a right triangle, with
a right ang...
a right ang...
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