Question

22. Given: angle DEH and angle EHG are supplementary, angle DFG and angle EHG are supplementaryProve: DF/FG = EH/FG Please give 8 Statements and Reasons

Answer 1

The sum of supplementary angles is 180 degrees. There,fore

`\begin{gathered} <\text{DEH}+<\text{EHG}=180^(\circ)\ldots.(1) \\ \end{gathered}`

So, Also, since angle DFG and angle EHG are supplementary,

So, From (2) and (3), we get

In triangles DEH and DFG, Therefore, in triangles DEH and DFG, two angles are equal. If two corresponding angles of two triangles are equal, third angle will also be equal. Hence,

Since all the angles of triangle DEH are equal to all the angles of triangle DFG, the triangles are similar.

For similar triangles, the ratio of sides opposite to corresponding angles are equal. Therefore, wecan write

`(DE)/(DF)=(EH)/(FG)`