in a triangle ABC, right angled at B, BD is drawn perpendicular to AC prove that angle ABD = angle - Maths -

Question

in a triangle ABC, right angled at B, BD is drawn perpendicular
to AC prove that angle ABD = angle C and angle CBD= angle A

Manbar Singh · Accepted Answer

GIVEN :ABC is a right ∆, in which ∠B = 90°
Also, BD⊥AC TO PROVE :1
∠ABD = ∠C2
∠CBD = ∠APROOF :In ∆ ADB,∠A + ∠ADB + ∠ABD = 180°       Angle sum property⇒∠A + 90° + ∠ABD = 180°⇒∠ABD + ∠A = 90°   
1In ∆ CDB,∠C + ∠CDB + ∠DBC = 180°       Angle sum property⇒∠C + 90° + ∠DBC = 180°⇒∠DBC + ∠C = 90°   
2Now, in ∆ABC,∠ABC = 90°⇒∠ABD + ∠DBC = 90°⇒∠ABD + ∠DBC = ∠ABD + ∠A   using 1⇒∠DBC = ∠AAgain,In ∆ABC,∠ABC = 90°⇒∠ABD + ∠DBC = 90°⇒∠ABD + ∠DBC =∠DBC + ∠C  using 2⇒∠ABD = ∠C

in a triangle ABC, right angled at B, BD is drawn perpendicular to AC.prove that angle ABD = angle C. and angle CBD= angle A