The Total solution for NCERT class 6-12
In ΔABC, AD is the perpendicular bisector of BC (see thegiven figure). Show that ΔABC is an isosceles triangle in which AB = AC.
In ΔADC and ΔADB,
AD = AD (Common)
∠ADC =∠ADB (Each 90º)
CD = BD (AD is the perpendicular bisector of BC)
∴ ΔADC ≅ ΔADB (By SAS congruence rule)
∴AB = AC (By CPCT)
Therefore, ABC is an isosceles triangle inwhich AB = AC.