St abd uv are intersecting at a such that the lengths of os ot ou ov in (cm) are 4.2 6.3 1.2 and 1.8 prove su parallel vt
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In Δ SOU and Δ TOV we have
SO = OT [∴ O is the mid point of ST]
∠ SOU = ∠ TOV [Vertically opposite angles]
and, UO = OV [∵ O is the mid point of UV]
So by SAS congruence criterion, we have
Δ SOU ≡ Δ TOV
SU = VT and ∠ USO = ∠ VTO [Corresponding parts of congruent triangle are equal]
Now, SU and VT are two lines intersected by a transversal ST such that ∠USO = ∠ VTO, i.e. alternative angles are equal.
Therefore SU is parallel to VT.
SO = OT [∴ O is the mid point of ST]
∠ SOU = ∠ TOV [Vertically opposite angles]
and, UO = OV [∵ O is the mid point of UV]
So by SAS congruence criterion, we have
Δ SOU ≡ Δ TOV
SU = VT and ∠ USO = ∠ VTO [Corresponding parts of congruent triangle are equal]
Now, SU and VT are two lines intersected by a transversal ST such that ∠USO = ∠ VTO, i.e. alternative angles are equal.
Therefore SU is parallel to VT.
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in Δs SOU and TOV, ∠UOS = ∠VOT (vertical angles)
We know UO || OV and OS || OT.
let us see the ratio of these sides:
OV/OT = 1.8/6.3 = 2/7
OU / OS = 1.2 / 4.2 = 2/7
As the ratios are equal also, it means both triangles are similar as included angle is same and the ratio of corresponding parallel sides is equal.
So SU || VT.
We know UO || OV and OS || OT.
let us see the ratio of these sides:
OV/OT = 1.8/6.3 = 2/7
OU / OS = 1.2 / 4.2 = 2/7
As the ratios are equal also, it means both triangles are similar as included angle is same and the ratio of corresponding parallel sides is equal.
So SU || VT.
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