⦁ Complete the proof of the Pythagorean theorem.

⇒ a²+b² = c²

Step-by-step explanation:

in ΔBCD and ΔBAC∠BDC = ∠ACB (90° each)∠CBD =∠CBA (common)by AA similarity criteriaΔBCD  is similar to ΔBACBC/BA = CD/AC = BD/BC ( by similarity creteria)BC/BA =BD/BCBC² = BD* BA (equation 1)Again, in ΔACD & ΔABC∠CDA = ∠ACB (90° each)∠CAD = ∠CAB (common)By AA similarity criteriaΔACD is similar to ΔABCAC/AB = CD/BC = AD/AC (by similarity criteria)AC/AB = AD/ACAC² = AD·AB (equation 2)Adding equation 1 & equation 2BC²+AC² = (BD.BA) + (AD.AB)BC²+AC² = AB(BD+AD)BC²+AC² = AB.AB   (BD+AD=AB)BC²+AC² = AB²⇒ a²+b² = c²Hence Proved

  The number of balloons varies directly with the number of tables. The two variables are directly proportional. The relationship of balloons to tables is the ratio 5:1, where 5 is the constant of variation. Use the equation y = kx, where k is the constant of variation resulting in the equation y = 5x.

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