Gujarat BoardEnglish MediumSTD 9MathsTriangles2 Marks
Question
In figure, AC = AE, AB = AD and $\angle$BAD = $\angle$EAC. Show that BC = DE.
✓
Answer
Given : AC = AE, AB = AD and $\angle$BAD = $\angle$EAC. To prove ; BC = DE Proof : In DABC and DADE AC = AE, AB = AD and ∠BAD = ∠EAC ...[Given] $\therefore$ $\angle$BAD + $\angle$DAC = $\angle$DAC + $\angle$EAC ...[Adding $\angle$DAC to both sides] $\therefore$ $\angle$BAC = $\angle$DAE ...(1) AC = AE ...[Given] $\angle$BAC = $\angle$DAE ...[From (1)] AB = AD ...[Given] $\therefore$ DABC $\cong$ DADE ...[By SAS property] $\therefore$ BC = DE ...[c.p.c.t.]
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