Mathematics
In the given figure, the sides BA and CA of △ABC have been produced to D and E such that BA = AD and CA = AE. Prove that, ED || BC.
Triangles
4 Likes
Answer
In △ABC and △ADE,
⇒ AB = AD [Given]
⇒ AC = AE [Given]
⇒ ∠BAC = ∠EAD [Vertically opposite angles are equal]
∴ △ABC ≅ △ADE [By S.A.S axiom]
⇒ ∠ABC = ∠ADE [Corresponding parts of congruent triangles are equal.]
From figure,
∠ABC and ∠ADE are alternate angles and since they are equal.
∴ ED || BC
Hence, proved that ED || BC.
Answered By
2 Likes
Related Questions
In the given figure, PA ⊥ AB; QB ⊥ AB and PA = QB. If PQ intersects AB at M, show that M is the mid-point of both AB and PQ.
AB is a line segment. AX and BY are two equal line segments drawn on opposite sides of AB such that AX || YB. If AB and XY intersect at M, prove that :
(i) △AMX ≅ △BMY
(ii) AB and XY bisect each other at M.
In the given figure, the line segments AB and CD intersect at a point M in such a way that AM = MD and CM = MB. Prove that, AC = BD but AC may not be parallel to BD.
If two altitudes of a triangle are equal, prove that it is an isosceles triangle.
