Naomi used the figure shown below to help prove the Pythagorean Theorem. In the figure, both ∆ACD and ∆CBD are similar to ∆ABC. She began by correctly setting up the proportions a/c=x/a and b/c=y/b and cross-multipling to get the equations a^2=xc and b^2=yc. What should Naomi do next? Select options from the drop-down menus to correctly complete each sentence. First, she should find the --- A.) sum B.) Difference C.) Product D.) Quotient of the equations a^2=xc and b2=yc to get another equation. Then she should factor one of the sides of the resulting equation. Finally, she should substitute --- A.) A B.) B C.) C into the resulting equation and multiply. This will prove the Pythagorean Theorem.
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Naomi used the figure shown below to help prove the Pythagorean Theorem. In the figure, both ∆ACD and ∆CBD are similar to ∆ABC.
She began by correctly setting up the proportions a/c=x/a and b/c=y/b and cross-multipling to get the equations a^2=xc and b^2=yc. What should Naomi do next? Select options from the drop-down menus to correctly complete each sentence.
First, she should find the ---
A.) sum
B.) Difference
C.) Product
D.) Quotient
of the equations a^2=xc and b2=yc to get another equation. Then she should factor one of the sides of the resulting equation. Finally, she should substitute ---
A.) A
B.) B
C.) C
into the resulting equation and multiply. This will prove the Pythagorean Theorem.
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