Question

In triangle ABC, X is any point on AC. If Y, Z, U and Y are the middle points of AX, XC, AB and BC respectively, then prove that UY || VZ and UV|| YZ


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Answer 1

Answer:

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

BVNVC = XZ/ZC

Now we will converse BPT

BX II 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 II 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