Provide the missing reasons for the proof given <C <E prove: ∆ABC ~DBE
2 answers:
For two triangles to be similar.
The ratio of their sides must be in proportion.(SSS)
Any two angles of one triangle must be equal to two angles of another triangle. (AA)
Ratio of two sides must be in proportion and the included angles must be congruent.
Here in the figure it is given that
<C = <E
Also
<ABC = <DBE as they are vertical angles.
So by AA
ΔABC ~ ΔDBE.
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I would start by setting up a chart like I did below.
Label one column age now and the other age in 5 years.
Since we don't know the son's age we use x.
We do know that the man's age is 4 times the son's age.
So the man's age will be 4x.
In the age in 5 year column, we add 5 to their current ages.
Now set up our equation.
Since it says "in five years" we use information in second column.
In 5 years time, he, "4x + 5", will be, equals,
3 times as old as his son, "3(x + 5)".
So we have 4x + 5 = 3(x + 5).
Solving from here, we find that x = 10.
So the son is 10 and the man is 4 times his age or 40.
