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The Given Figure Shows a Triangle Abc in Which Ad Bisects Angle Bac. Eg is Perpendicular Bisector of Side Ab Which Intersects Ad at Point F. Prove That: - Mathematics

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Sum

The given figure shows a triangle ABC in which AD bisects angle BAC. EG is perpendicular bisector of side AB which intersects AD at point F.
Prove that: 

(ii) F is equidistant from AB and AC.

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Solution

 

Construction: Draw LF ⊥ AC
Proof: In Δ AFL and ΔAFE,
∠FEA = ∠FLA (Each = 90°)
∠LAF = FAE (AD bi sects ∠BAC)
AF = AF (common)
∴ By angle – Angle side criterion of congruence,
ΔAFL ≅ AFE (AAS postulate)
The corresponding parts of the congruent triangles are congruent.
∴ FE = FL (CPCT)
Hence, F is equidistant from AB and AC.  

Concept: Theorems Based on Loci
  Is there an error in this question or solution?

APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 16 Loci (Locus and Its Constructions)
Exercise 16 (A) | Q 11.2 | Page 238

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