If in triangles $X Y Z, X Y = X Z$ and $M, N$ are the midpoints of $X Y, Y Z$ and which one of the following is correct?

M N = Y Z

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N Y = N Z = M N

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M X = M Y = N Y

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M N = M X = M Y

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Solution

The correct option is D $M N = M X = M Y$
$M X = M Y, X Y = X Z$ and $M N ∥ X Z$
$\Rightarrow ∠ X Z Y = ∠ M N Y \Rightarrow ∠ M Y N = ∠ M N Y$
$\Rightarrow M N = M Y$ also $M Y = M X (∵ ∠ y = ∠ z)$
$\Rightarrow M N = M Y = M X$

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Similar questions

Q. If in triangle

X Y Z, X Y = X Z

and

M, N

are the mid points of

X Y, Y Z,

then which one of the following is correct?

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X Y Z, X Y = X Z

and M, N are the mid points of XY YZ, then which one of the following is orrect ?

Q. Eliminate

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There are two triangles ABC and XYZ such that ΔABC ΔYXZ. their measurement are given as follows: AB =6 cm, AC = 9 cm, BC = 7 cm. Find out the corresponding measurements of triangle YXZ.

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If in triangles XYZ,XY=XZ and M,N are the midpoints of XY,YZ and which one of the following is correct?

The correct option is D MN=MX=MYMX=MY,XY=XZ and MN∥XZ⇒∠XZY=∠MNY⇒∠MYN=∠MNY⇒MN=MY also MY=MX(∵∠y=∠z)⇒MN=MY=MX

If in triangles $X Y Z, X Y = X Z$ and $M, N$ are the midpoints of $X Y, Y Z$ and which one of the following is correct?

The correct option is D $M N = M X = M Y$
$M X = M Y, X Y = X Z$ and $M N ∥ X Z$
$\Rightarrow ∠ X Z Y = ∠ M N Y \Rightarrow ∠ M Y N = ∠ M N Y$
$\Rightarrow M N = M Y$ also $M Y = M X (∵ ∠ y = ∠ z)$
$\Rightarrow M N = M Y = M X$