In ∆ ABC, AD is the perpendicular bisector of BC (see Fig. 7.30). Show that ∆ ABC is an isosceles triangle in which AB = AC.
In ∆ ABC, AD is the perpendicular bisector of BC (see Fig. 7.30). Show that ∆ ABC is an isosceles triangle in which AB = AC.
Solution and Explanation
In ∆ADC and ∆ADB,
AD = AD (Common)
∠ADC = ∠ADB (Each 90º)
CD = BD (AD is the perpendicular bisector of BC)
∠∆ADC ∠∆ADB (By SAS congruence rule)
∴ AB = AC (By CPCT)
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