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D, E, and F are the mid-points of the sides AB, BC and CA of an isosceles ΔABC in which AB = BC. Prove that ΔDEF is also isosceles.

D, E, and F are the mid-points of the sides AB, BC and CA of an isosceles ΔABC in which AB = BC.

Prove that ΔDEF is also isosceles.

Sum

DF = `1/2`BC ...(i)

DE = `1/2`AC ...(ii)

EF = `1/2`AB

EF = `1/2`BC ...(iii) ...[AB = BC]

From equation (i) & (ii)

DF = EF

Hence, DEF is also isosceles triangle.

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Chapter 11: Mid-point Theorem and Its Converse [Including Intercept Theorem] - Exercise 11 (A) [Page 168]

Chapter 11 Mid-point Theorem and Its Converse [Including Intercept Theorem]
Exercise 11 (A) | Q 4. | Page 168

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