In triangle ADE shown In Flguro 14.92 , the point B Is haltway from A to D and the point C is halfway from A to E. Compare the areas of triangles ABC and ADE. Explain your reasoning clearly. .
Figure 14.92 Triangles
To compare: The areas of triangles ABC and ADE .
Explanation of Solution
Consider the diagram as shown below.
In the above Figure 1 point B is midpoint of AD and C is the midpoint of AE.
In the triangle ABC and ADE ,
The angle A is common.
Since
Similarly, ACB and AED is equal.
Therefore, triangle ABC and ADEis similar triangles.
The ration of the areas of the similar triangle is equal to the square of the ratio of the corresponding side.
Consider
Therefore, the ration of areas of the triangle is,
Substitute,
Therefore, the areas of the triangle are related as in the ratio of
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Chapter 14 Solutions
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