Maths-
General
Easy
Question
Triangles ABC and DEF above are similar. How much longer than segment EF is segment DE ?
- 1
- 2
- 4
- 8
Hint:
Hint:
To find the difference between DE and EF, first we need to find DE and EF. To find them, we use the properties of similarity of triangles. Two triangles are said to be similar if their corresponding angles are equal and the ratio of their corresponding sides is equal. We will get equality by using this second property and from there, we can calculate the values of DE and EF.
The correct answer is: 2
Given,
∆ABC and ∆DEF are similar.
By the property of similar triangles, we now that the corresponding sides have the same ratio, that is,
∆ABC and ∆DEF are similar.
By the property of similar triangles, we now that the corresponding sides have the same ratio, that is,
We are also given that,
Inputting these values in the expression above, we get
Simplifying it, we have
From the first and the third values, we get,
Thus, the value of DE is given by
Similarly, from the second fraction, we have,
Thus, the value of EF is given by
Now,
Thus, DE is longer than EF by 2
The correct option is B)
Note:
There are three ways to prove that two triangles are similar- AAA,
SAS, SSS.
AAA means that the corresponding angles are equal,
SAS means two sides of the triangles are in equal ratio and the angles between these two sides are equal,
SSS means that all three corresponding sides have equal ratio
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