Question 2:
In ∆ABC, AD is the perpendicular bisector of BC (see the given figure). Show that
∆ABC is an isosceles triangle in which AB = AC.
Answer:
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)
Therefore, ABC is an isosceles triangle in which AB = AC.
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