ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Fig). Show that (i) ∆ ABE ≅ ∆ ACF (ii) AB = AC, i.e., ABC is an isosceles triangle.

Question

ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Fig). Show that  (i) ∆ ABE ≅ ∆ ACF  (ii) AB = AC, i.e., ABC is an isosceles triangle.

cdquestions Admin · Accepted Answer

(i) In ∆ABE and ∆ACF,  ∠ABE and ∠ACF (Each 90º)  ∠A = ∠A (Common angle)  BE = CF (Given)  ∠∆ABE  ∠∆ACF (By AAS congruence rule)  (ii) It has already been proved that  ∠∆ABE  ∠∆ACF  ∴ AB = AC (By CPCT)

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

ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Fig). Show that
(i) ∆ ABE ≅ ∆ ACF
(ii) AB = AC, i.e., ABC is an isosceles triangle.

Solution and Explanation

Top CBSE Class IX Mathematics Questions

Top CBSE Class IX Questions