Question

1. the figure on the left reflects, or flips, over a line of reflection to create the figure on the right. describe the effect on the reflection and determine the location of the line of reflection.

spaced practice

1. determine whether the equation ( a^2 + b^2 = c^2 ) is true for the given values of ( a ), ( b ), and ( c ).

a. ( a = 4 ), ( b = 3 ), and ( c = 5 )
b. ( a = 24 ), ( b = 7 ), and ( c = 25 )

Explanation:

Part a:

Step1: Calculate \(a^2\), \(b^2\), \(c^2\)

\(a = 4\), so \(a^2=4^2 = 16\); \(b = 3\), so \(b^2 = 3^2=9\); \(c = 5\), so \(c^2=5^2 = 25\)

Step2: Check \(a^2 + b^2\) vs \(c^2\)

\(a^2 + b^2=16 + 9=25\), and \(c^2 = 25\). So \(a^2 + b^2=c^2\) holds.

Part b:

Step1: Calculate \(a^2\), \(b^2\), \(c^2\)

\(a = 24\), so \(a^2=24^2=576\); \(b = 7\), so \(b^2 = 7^2 = 49\); \(c = 25\), so \(c^2=25^2=625\)

Step2: Check \(a^2 + b^2\) vs \(c^2\)

\(a^2 + b^2=576+49 = 625\), and \(c^2=625\). So \(a^2 + b^2=c^2\) holds.

Answer:

a. The equation \(a^{2}+b^{2}=c^{2}\) is true (since \(4^{2}+3^{2}=16 + 9=25=5^{2}\)).
b. The equation \(a^{2}+b^{2}=c^{2}\) is true (since \(24^{2}+7^{2}=576 + 49=625=25^{2}\)).