To Determine:
So, here is the complete proof of the Pythagorean theorem.
Given: Δ ABC is a right triangle, with
a right angle at ∠C
Prove: A²+B² =C²
Answer:
Note: All the answers for the questions marks are filled with in bold text.
Statement
1. ΔABC is a right triangle, with a right angle at ∠C
2. Draw an altitude from point C to line AB
3. ∠CDB and ∠CDA are right angles.
4. ∠BCA ≅ ∠BDC
5. ∠B ≅ ∠B
6. AA Similarity Postulate
7. [tex]\frac{a}{x}\:=\:\frac{c}{a}[/tex]
8. a² = cx
9. ∠CDA ≅ ∠BCA
10. ∠A ≅ ∠A
11. ΔCBA ~ ΔDBA
12. [tex]\frac{b}{y}\:=\:\frac{c}{b}[/tex]
13. b² = cy
14. a² + b² = cx + cy
15. [tex]\left(CB\right)^2+\left(CA\right)^2=\left(AB\right)\left(DB+BA\right)[/tex]
16. x + y = c
17. a² + b² = c²
Reason
1. Given
2. From a point not on a line, exactly one perpendicular can be drawn through the point to the line.
3. Definition of altitude
4. All right angles are congruent.
5. Reflexive Property
6. AA Similarity Postulate
7. Polygon Similarity Postulate
8. Cross Multiply and Simplify
9. All right angles are Congruent
10. Reflexive Property
11. AA similarity Postulate
12. Polygon Similarity Postulate
13. Cross Multiply and Simplify
14. Addition Property of Equality
15. Distributive Property
16. Segment Addition Postulate
17. Substitution Property
Keywords: statement, reason
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