Question

(Hul. Upu
T
9. In the adjacent figure triangle ABC, D is the midpoint if BC. DE is perpendicular to AB,DF is perpendicular to AC and DE=DF. Show that ∆BED is congruent to ∆CFD​

Answer 1

Answer:

Given data:

In ∆ABC,

D is the midpoint of BC

∴ BD = DC ….. (i)

DE ⊥ AB ….. (ii)

DF ⊥ AC ….. (iii)

DE = DF ….. (iv)

To show: ∆BED is congruent to ∆CFD

In ∆BED and ∆CFD, we have

BD = DC [from (i)]

∠BED = ∠CFD = 90° [from (ii) & (iii)]

DE = DF [from (iv)]

Thus, by RHS congruence i.e., Right-angle-Hypotenuse-Side congruence in which, if two right-angled triangles have their hypotenuses and a pair of shorter sides are equal in length then the triangles congruent, we can say

∆BED ≅ ∆CFD

Hence proved  

Answer 2

Answer:

Step-by-step explanation:

Given: 1) BD=DC

2)DE is perpendicular to AB

3) DF is perpendicular to AC

4) DE= DF

R.T.P : ∆ BED is congruent to ∆ CFD

Proof: In ∆ BED and ∆ CFD

BD= DC( from 1)

Angle BED = Angle CFD

DE = DF( from 4)

Therefore,∆ BED is cogruent to ∆ CFD {SAS congruence rule}