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Standard X

Mathematics

Angles in Alternate Segments

Lines l and...

Question

Lines $l$ and $m$ are the lines of symmetry of the line segment $X Y$ and $Y Z$ respectively. If $X A = 4 c m$ and $Y Z = 6 c m$ , find $A Y, Y B, X Z$ .

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Solution

Given $l, m$ are the lines of symmetryof line segment $X Y$ and $Y Z$
$⟹ A Y = X A, Y B = B Z$
SO $A Y = X A = 4 c m, Y B = B Z$
$Y Z = 6 c m ⟹ Y B = B Z = 3 c m$
$X Z = X A + A Y + Y B + B Z = 2 (X A) + Y Z = 2 \times 4 + 6 = 14 c m$

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Lines l and m are the lines of symmetry of the line segment XY and YZ respectively. If XA=4 cm and YZ=6 cm, find AY, YB, XZ.

Given l,m are the lines of symmetryof line segment XY and YZ⟹AY=XA,YB=BZSO AY=XA=4 cm,YB=BZYZ=6 cm⟹YB=BZ=3 cmXZ=XA+AY+YB+BZ=2(XA)+YZ=2×4+6=14 cm

Lines $l$ and $m$ are the lines of symmetry of the line segment $X Y$ and $Y Z$ respectively. If $X A = 4 c m$ and $Y Z = 6 c m$ , find $A Y, Y B, X Z$ .

Given $l, m$ are the lines of symmetryof line segment $X Y$ and $Y Z$
$⟹ A Y = X A, Y B = B Z$
SO $A Y = X A = 4 c m, Y B = B Z$
$Y Z = 6 c m ⟹ Y B = B Z = 3 c m$
$X Z = X A + A Y + Y B + B Z = 2 (X A) + Y Z = 2 \times 4 + 6 = 14 c m$