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Home » 8. In the fig.4.142 given, if AB ⊥ BC, DC ⊥ BC, and DE ⊥ AC, prove that ΔCED ∼ ΔABC
8. In the fig.4.142 given, if AB ⊥ BC, DC ⊥ BC, and DE ⊥ AC, prove that ΔCED ∼ ΔABC
CBSE | Class 10 | Exercise 4.5 | Maths | Maths | RD Sharma | Triangles
8. In the fig.4.142 given, if AB ⊥ BC, DC ⊥ BC, and DE ⊥ AC, prove that ΔCED ∼ ΔABC

Solution:

Given:

AB ⊥ BC,

DC ⊥ BC,

DE ⊥ AC

To prove:

 ΔCED∼ΔABC

From ΔABC and ΔCED

∠B = ∠E = 90o   [given]

∠BAC = ∠ECD     (alternate angles since, AB || CD with BC as transversal)

Therefore, ΔCED∼ΔABC (AA similarity)

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