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Question
Observe all the four triangles FAB, EAB, DAB and CAB as shown in the following figure.
- All triangles have the same base and the same altitude.
- All triangles are congruent.
- All triangles are equal in area.
- All triangles may not have the same perimeter.
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Solution
1. True.
It is clear from the figure that all triangles have same base AB and all the vertices lie on the same line, so the distance between vertex and base of triangle (i.e. length of altitude) are equal.
2. False
It is clear from the figure that all triangles have only base line is equal and no such other lines are equal to each other.
3. True
Because the triangles on same base and between same parallel lines have equal in area.
4. True
It is clear from the figure that all triangles may not have the same perimeter.
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