The correspondence ABC⇔ ZXY is a similarity in ΔABC and ΔXYZ. If AB=12,BC=9, CA=7.5 and ZX=10, then YZ+XY=.....,Fill in the blank so that the given statement is true.
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Given: The correspondence ABC ↔ ZXY is a similarity in ∆ABC and ∆XYZ.
AB = 12,
BC = 9,
CA = 7.5 &
ZX = 10
To find: YZ + XY = ?
by definition, for a given correspondence between the vertices of two triangles, if the corresponding angles of the triangles are congruent and the lengths of the corresponding sides are in proportion, then the given correspondence is a similarity between two triangles.
⇒AB/ZX = BC/XY = CA/YZ
⇒AB/ZX = BC/XY = CA/YZ = (BC + CA)/(XY + YZ)
⇒ AB/ZX = (BC + CA)/(XY + YZ)
reciprocating both sides,
⇒(XY + YZ)/ZX = (BC + CA)/AB
⇒(XY + YZ) = ZX × (BC + CA)/AB
= 10 × (9 + 7.5)/12
= 13.75
hence, (XY + YZ) = 13.75
AB = 12,
BC = 9,
CA = 7.5 &
ZX = 10
To find: YZ + XY = ?
by definition, for a given correspondence between the vertices of two triangles, if the corresponding angles of the triangles are congruent and the lengths of the corresponding sides are in proportion, then the given correspondence is a similarity between two triangles.
⇒AB/ZX = BC/XY = CA/YZ
⇒AB/ZX = BC/XY = CA/YZ = (BC + CA)/(XY + YZ)
⇒ AB/ZX = (BC + CA)/(XY + YZ)
reciprocating both sides,
⇒(XY + YZ)/ZX = (BC + CA)/AB
⇒(XY + YZ) = ZX × (BC + CA)/AB
= 10 × (9 + 7.5)/12
= 13.75
hence, (XY + YZ) = 13.75
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