 Hello and welcome to the session. Let's work out the following problem It says P is a point in the interior of triangle A, B, C, X, Y and Z are points on the lines P, A, P, B and P, C respectively So that X, Y is parallel to A, V and X, Z is parallel to A, C prove that Y, Z is parallel to B, C So this is the figure we need to refer we are given a triangle A, B, C and P is the interior point and X, Y and Z are the points on the line P, A, P, B and P, C respectively So that X, Y is parallel to A, V, X, Z is parallel to A, C and we have to prove that Y, Z is parallel to B, C So let's now move on to the solution Let's first write what is given to us A triangle A, B, C P is the interior point X, Y is parallel to A, B And X, Z is parallel to A, C Let's now write what we have to prove We have to prove that Y, Z is parallel to B, C Now we have to prove that Y, Z is parallel to B, C For that we will use the converse of the basic proportionality theorem Which says that if the ratio P, Y upon B, Y is equal to P, Z upon Z, C Then Y, Z is parallel to B, C So let's now start the proof Now in triangle A, P, B, X, Y is parallel to A, B This is given to us Therefore by the basic proportionality theorem That is, V, P, T, A, X Upon X, P Is equal to V, Y Upon Y, P Let's name this as one Now in triangle A, P, C X, Z is parallel to A, C Therefore A, X Upon X, P Is equal to C, Z Upon Z, P Let's name this as two Now A, X upon X, P is equal to B, Y upon Y, P And also A, X upon X, P is equal to C, Z upon Z, P So from one and two We have B, Y Upon Y, P Is equal to C, Z upon Z, P So this implies Y, Z is parallel to B, C By the converse of B, P, T Hence the result is proved So this completes the question Do remember to use the basic proportionality theorem And it's converse So bye for now, take care and have a good day