Question

BE is perpendicular to DA and CD is perpendicular to DA then prove that m angle 1 is congruent to m angle 3​

Answer 1

Answer:

∠1 = ∠3

Step-by-step explanation:

∠AEB = 90°  as BE ⊥ DA

∠EDC = 90° as CD ⊥ DA

∠EDC = ∠EDB + ∠BDC

=> 90° = ∠EDB  + ∠1    Eq1

in ΔDBE

∠AEB = ∠EBD + ∠EDB   ( External angle of triangle = Sum of other two internal angles)

=> 90° = ∠3 + ∠EDB    Eq2

Equating eq1 & eq2

∠EDB  + ∠1 = ∠3 + ∠EDB

cancelling ∠EDB from both sides

=> ∠1 = ∠3

Hence Proved that m angle 1 is congruent to m angle 3​