Question

in the figure xy parallel to BC show that a x by a b is equal to a y by AC is equal to X Y by ac

Answer 1

Here, I add figure in which XY || BC
now, from ∆AXY and ∆ABC
here it is clear that , ∠AXY = ∠ABC
and ∠AYX = ∠ACB
and ∠BAC is common angle for both the given triangle.
so, from A - A - A rule of similarity,
∆AXY $\sim$ ∆ABC
we know, if two triangles are similar then ratio of corresponding sides of triangles are equal.
e.g., AX/AB = AY/AC = XY/BC [hence proved]

Answer 2

Given: XY is parallel to BC

To prove= AX/AB = AY/AC = XY/AC

Solution:

• Now, we know that XY is parallel to BC,

• Lets consider the triangle AXY and triangle ABC,

• In ∆AXY and ∆ABC

• We can see that

             ang AXY = ang ABC......... (corresponding angles)

             ang AYX = ang ACB..........(corresponding angles)

             ang BAC = ang BAC .........( common angle)

• So, from AAA rule of similarity,  (Angle Angle Angle)

             triangle AXY is similar to triangle ABC.

• Now,

• We have the theorem that states: the ratio of corresponding sides of triangles are equal, if two triangles are similar.

Answer:

• So by this theorem we can conclude that,

               AX/AB = AY/AC = XY/BC

                Hence proved