Question

In the given triangle ABC, AD is the perpendicular bisector of BC. Identify the congruent triangles and give reasons. What type of triangle is triangle ABC?



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Answer 1

Answer:

If in ΔABC, AD is the perpendicular bisector of BC, then we have proved that ΔABC is an isosceles triangle in which AB = AC.

Step-by-step explanation:

Solution:

Given: AD is the perpendicular bisector of BC means ∠ADB = ∠ADC = 90° and BD = DC

In ΔADC and ΔADB,

AD = AD (Common)

∠ADC = ∠ADB (Each 90°)

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 in which AB = AC.