Mathematics
In context of the adjoining figure, name
(i) all triangles
(ii) all triangles having point E as common vertex.
Geometrical Concepts
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Answer
In the given figure, we have two overlapping triangles △ABC and △DBC sharing the common base BC. The line segments AC and BD intersect each other at point E in the interior of the figure.
(i) Looking carefully at the figure, the line segments drawn are AB, BC, CA, BD and DC. These line segments, along with the intersection point E, form the following triangles:
- △ABC (formed by sides AB, BC and CA)
- △DBC (formed by sides DB, BC and CD)
- △ABE (formed by sides AB, BE and EA)
- △BEC (formed by sides BE, EC and CB)
- △CDE (formed by sides CD, DE and EC)
∴ The five triangles in the figure are △ABC, △DBC, △ABE, △BEC and △CDE.
(ii) Point E is the intersection point of segments AC and BD. A triangle has point E as a vertex only if two of its sides meet at E.
The triangles having point E as common vertex are △ABE, △BEC and △CDE.
∴ The triangles having point E as common vertex are △ABE, △BEC and △CDE.
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