In isosceles triangle ABC,AB =AC DandEare point on BC such that BE=CD SHOW THAT AD=AE
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Answered by
5
Given that AB = AC. Therefore ABC is an isosceles triangle.
Also given that AD = AE.
We need to prove that B,C,D and E are concyclic.
Since AB = AC and AD = AE, we have BD = DE.
If a line divides any two sides of a triangle in the same ratio, then the line must be parallel tothe third side.
Thus, the line DE is parallel to the side BC.
In triangle ABC, since AB = AC, we have

In triangle ADE, since AD = AE, we have

Thus in triangle ABC and ADE, we have,
and
Using equations (1) and (2), the above equations become
and

If the sum of any pair of opposite angles of a quadrilateral is 180 degrees, then the quadrilateral is cyclic.
Since the anglesare opposite angles of the quadrialteral BCED, then the quadrilateral is cyclic.
Also given that AD = AE.
We need to prove that B,C,D and E are concyclic.
Since AB = AC and AD = AE, we have BD = DE.
If a line divides any two sides of a triangle in the same ratio, then the line must be parallel tothe third side.
Thus, the line DE is parallel to the side BC.
In triangle ABC, since AB = AC, we have

In triangle ADE, since AD = AE, we have

Thus in triangle ABC and ADE, we have,
and
Using equations (1) and (2), the above equations become
and

If the sum of any pair of opposite angles of a quadrilateral is 180 degrees, then the quadrilateral is cyclic.
Since the anglesare opposite angles of the quadrialteral BCED, then the quadrilateral is cyclic.
Answered by
17
We have, AB= AC, thus angleB = angleC
In triangle, ABE and ACD
AB = AC
angle B = C
BE = CD
therefore, triangle ABE = ACD
thus, AD = AE ( CPCT )
Plz mark as brainliest
In triangle, ABE and ACD
AB = AC
angle B = C
BE = CD
therefore, triangle ABE = ACD
thus, AD = AE ( CPCT )
Plz mark as brainliest
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