Question

kamryn
part a
point c has the coordinates (5,5). which proportions show that the slopes of the hypotenuses of the triangles are equivalent?
select true or false for each proportion.
\\( \frac { e d } { d c } = \frac { c a } { a b } \\) true false
\\( \frac { c a } { a b } = \frac { c d } { d e } \\) true false
\\( \frac { 5 - 2 } { 5 - 1 } = \frac { c a } { a b } \\) true false
\\( \frac { 5 - 1 } { 5 - 2 } = \frac { 1 7 - 5 } { a b } \\) true false

Explanation:

Step1: Calculate the lengths

• For \(ED\): \(ED = 5 - 2=3\)
• For \(DC\): \(DC = 5 - 1 = 4\)
• For \(CA\): \(CA = 5 - 1=4\)
• For \(AB\): \(AB = 5 - 1 = 4\)

Step2: Check the first proportion \(\frac{ED}{DC}=\frac{CA}{AB}\)

• \(\frac{ED}{DC}=\frac{3}{4}\)
• \(\frac{CA}{AB}=\frac{4}{4} = 1\)
• \(\frac{3}{4}

eq1\)

Step3: Check the second proportion \(\frac{CA}{AB}=\frac{CD}{DE}\)

• \(\frac{CA}{AB}=\frac{4}{4}=1\)
• \(\frac{CD}{DE}=\frac{4}{3}\)
• \(1

eq\frac{4}{3}\)

Step4: Check the third proportion \(\frac{5 - 2}{5 - 1}=\frac{CA}{AB}\)

• \(\frac{5 - 2}{5 - 1}=\frac{3}{4}\)
• \(\frac{CA}{AB}=\frac{4}{4} = 1\)
• \(\frac{3}{4}

eq1\)

Step5: Check the fourth proportion \(\frac{5 - 1}{5 - 2}=\frac{17 - 5}{AB}\)

• \(\frac{5 - 1}{5 - 2}=\frac{4}{3}\)
• \(AB = 4\), \(\frac{17 - 5}{AB}=\frac{12}{4}=3\)
• \(\frac{4}{3}

eq3\)

Answer:

\(\frac{ED}{DC}=\frac{CA}{AB}\): False

\(\frac{CA}{AB}=\frac{CD}{DE}\): False

\(\frac{5 - 2}{5 - 1}=\frac{CA}{AB}\): False

\(\frac{5 - 1}{5 - 2}=\frac{17 - 5}{AB}\): False