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15.Eis the mid-point of the non-parallel side BC of a trapezium ABCD.E is joined to the opposite vertices A and D. Prove that qquad ar(Delta ABE) ar(Delta DCE)=(1)/(2) ar (trapezium ABCD)?
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15.Eis the mid-point of the non-parallel side BC of a trapezium ABCD.E...
To prove that the area of triangle ABE is equal to half the area of trapezium ABCD, we can use the formula for the area of a trapezium:
Area of trapezium ABCD = (sum of lengths of parallel sides) x (height) / 2
Since E is the midpoint of side BC, we can call the length of side BC "2x" and the length of side AD "2y". We can also call the distance between points A and D "h".
Since E is the midpoint of side BC, we can call the length of side BC "2x" and the length of side AD "2y". We can also call the distance between points A and D "h".
Substituting these values into the formula for the area of a trapezium, we get:
Area of trapezium ABCD = (2x + 2y) x h / 2
Now, let's consider the area of triangle ABE. Since E is the midpoint of side BC, we know that the length of side AE is equal to x. We also know that the length of side AB is equal to y and the height of triangle ABE is equal to h.
Substituting these values into the formula for the area of a triangle (base x height / 2), we get:
Area of triangle ABE = xh / 2
Now, we can set the expression for the area of triangle ABE equal to half the expression for the area of trapezium ABCD and solve for x:
xh / 2 = (2x + 2y) x h / 4
x = y
This means that if the lengths of sides AB and AD are equal, then the area of triangle ABE is equal to half the area of trapezium ABCD.
The same logic can be applied to triangle DCE to prove that the area of triangle DCE is also equal to half the area of trapezium ABCD. Therefore, the overall result is:
Area of triangle ABE + Area of triangle DCE = 2 x (half the area of trapezium ABCD)
Which simplifies to:
Area of triangle ABE + Area of triangle DCE = Area of trapezium ABCD
Thus, we have proven that the area of triangles ABE and DCE is equal to the area of trapezium ABCD.
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15.Eis the mid-point of the non-parallel side BC of a trapezium ABCD.E is joined to the opposite vertices A and D. Prove that qquad ar(Delta ABE) ar(Delta DCE)=(1)/(2) ar (trapezium ABCD)?
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15.Eis the mid-point of the non-parallel side BC of a trapezium ABCD.E is joined to the opposite vertices A and D. Prove that qquad ar(Delta ABE) ar(Delta DCE)=(1)/(2) ar (trapezium ABCD)? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about 15.Eis the mid-point of the non-parallel side BC of a trapezium ABCD.E is joined to the opposite vertices A and D. Prove that qquad ar(Delta ABE) ar(Delta DCE)=(1)/(2) ar (trapezium ABCD)? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 15.Eis the mid-point of the non-parallel side BC of a trapezium ABCD.E is joined to the opposite vertices A and D. Prove that qquad ar(Delta ABE) ar(Delta DCE)=(1)/(2) ar (trapezium ABCD)?.
15.Eis the mid-point of the non-parallel side BC of a trapezium ABCD.E is joined to the opposite vertices A and D. Prove that qquad ar(Delta ABE) ar(Delta DCE)=(1)/(2) ar (trapezium ABCD)? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about 15.Eis the mid-point of the non-parallel side BC of a trapezium ABCD.E is joined to the opposite vertices A and D. Prove that qquad ar(Delta ABE) ar(Delta DCE)=(1)/(2) ar (trapezium ABCD)? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 15.Eis the mid-point of the non-parallel side BC of a trapezium ABCD.E is joined to the opposite vertices A and D. Prove that qquad ar(Delta ABE) ar(Delta DCE)=(1)/(2) ar (trapezium ABCD)?.
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