AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that (i) AD bisects BC (ii) AD bisects ∠A.

Question

AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that  (i) AD bisects BC  (ii) AD bisects ∠A.

cdquestions Admin · Accepted Answer

(i) In ∆BAD and ∆CAD,  ∠ADB = ∠ADC (Each 90º as AD is an altitude)  AB = AC (Given)  AD = AD (Common)  ∠∆BAD ≅ ∠∆CAD (By RHS Congruence rule)  BD = CD (By CPCT)  Hence, AD bisects BC.  (ii) Also, by CPCT,  ∠BAD = ∠CAD  Hence, ∠AD bisects A.

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that
(i) AD bisects BC
(ii) AD bisects ∠A.

Solution and Explanation

Top CBSE Class IX Mathematics Questions

Top CBSE Class IX Questions