Question

in triangle ABC, X is any point on AC. If Y,Z,U,V are middle point on AC,XC,AB and BC respectively,then prove that UY//UZ and UV//YZ

Answer 1

BV = VC -- (1) (V is the mid point of BC)

XZ = ZC -- (2) (Z is the  mid point of XC)

We will divide 1 by 2 we will get this:

BV/XZ = VC/ZC

BV/VC = XZ/ZC

Now we will converse BPT

BX || VZ -- (3)

AU = UB -- (4) (U is the midpoint of AB)

AY = YX -- (5) (Y is the mid point of AX)

Now we will divide 4 by 5 we will get this:

AU/AY = UB/YX

AU/UB = AY/YX

Now we will converse BPT

BX || UY -- (6)

From 3  and 6 we will get this

UY || VZ

Dividing 1 by 4 we will get this

BV/AU = VC/UB

BV/VC = AU/UB

By conversing of BPT

UV || AC

UV || YZ

Answer 2

Step-by-step explanation:

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