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In the figure, AB⎯⎯⎯⎯⎯ is parallel to DE⎯⎯⎯⎯⎯.Select from the drop-down menu to correctly complete the statement.TriangleABC and triangleDEC are :choices similar or not similar

In the figure AB is parallel to DESelect from the dropdown menu to correctly complete the statementTriangleABC and triangleDEC are choices similar or not simila class=

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Solution

In the diagram,

∠DCE = ∠ACB = 60 (vertically opposite angle are equal)

∠ABC = ∠CDE = 72 (alternate angle are equal)

∠BAC + ∠ACB + ∠CBA = 180

=> ∠BAC = 180 - ∠ACB - ∠CBA = 180 - 60 - 72 = 48

Also, ∠CED = ∠BAC = 48

SInce ∠A = ∠D, ∠B = ∠E and ∠C = ∠C

Hence △ABC is similar to △DEC

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