Step-by-step explanation:
Complete the proof of the Pythagorean theorem is given below.
Statement Reason
1. ΔABC is a right triangle, with a 1. Given
right angle at ∠C
2. Draw an altitude from point C 2. From a point not on a line, exactly
to AB one perpendicular can be drawn through the point to the line
3. ∠CDB and ∠CDA are right 3. Definition of altitude
angles
4. ∠BCA ≅ ∠BDC 4. All right angles are congruent
5. ∠B ≅ ∠B 5. [tex]Reflexive\:Property[/tex]
6. ΔCBA ~ ΔDBC 6. AA Similarity Postulate
7. [tex]\frac{a}{x}\:=\:\frac{c}{a}[/tex] 7. [tex]Polygon\:Similarity\:Postulate\:\:\:[/tex]
8. [tex]a^{2} = cx[/tex] 8. [tex]Cross\:Multiply\:and\:Simplify[/tex]
9. ∠CDA ≅ ∠BCA 9. [tex]All\:Right\:Angles\:are\:Congruent[/tex]
10. ∠A ≅ ∠A 10. [tex]Reflexive\:Property[/tex]
11. ΔCBA ~ ΔDBA 11. AA Similarity Postulate
12. [tex]\frac{b}{y}\:=\:\frac{c}{b}=[/tex] 12. [tex]Polygon\:Similarity\:Postulate[/tex]
13. [tex]b^2\:=\:cy[/tex] 13. [tex]Cross\:Multiply\:and\:Simplify[/tex]
14. [tex]a^2\:+\:b^2\:=\:cx\:+cy[/tex] 14. [tex]Addition\:Property\:of\:Equality[/tex]
15. [tex]\left(CB\right)^2+\left(CA\right)^2=\left(AB\right)\left(DB+BA\right)[/tex] 15. Distributive Property
16. [tex]x + y = c[/tex] 16. [tex]Segment\:Addition\:Postulate[/tex]
17. [tex]a^2\:+\:b^2\:=\:c^2[/tex] 18. [tex]Substitution\:Property[/tex]
