Question

How can use theorem 7-4 to find missing segments? (7-4 is similarity) :)

Answer 1

Given

AD = 6.4

BD = 3.6

Find

AC,BC and DC

Step-by-step explanation

Using Pythogoras theorem in triangle ADC

`AC^2=DC^2+6.4^2------(1)`

Using PT in triangle BDC

`BC^2=DC^2+3.6^2-------(2)`

Adding equation (1) and (2)

`\begin{gathered} AC^2+BC^2=DC^2+3.6^2+DC^2+6.4^2 \\ AC^2+BC^2=2DC^2+53.92 \end{gathered}`

Using PT in triangle ABC

`10^2=AC^2+BC^2`

Equating above 2 equations

`\begin{gathered} 100=2DC^2+53.92 \\ DC^2=23.04 \\ DC=4.8 \end{gathered}`

Putting this value of DC in equation (2)

`\begin{gathered} BC^2=4.8^2+3.6^2 \\ BC^2=23.04+12.96 \\ BC=6 \end{gathered}`

`\begin{gathered} 10^2=AC^2+BC^2 \\ 100=AC^2+36 \\ AC=8 \end{gathered}`

Final Answer

AC = 8

BC = 6

DC = 4.8