angle side angle postulate

# Angle Side Angle Postulate

Covid-19 has led the world to go through a phenomenal transition .

E-learning is the future today.

Stay Home , Stay Safe and keep learning!!!

Angle side angle postulate (ASA) - > If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent by angle-side-angle postulate. ∠B ≅ ∠E, BC ≅ EF and ∠C ≅ ∠F
∴ ΔABC ≅ Δ DEF by ASA

Examples :

1) Given : ∠BAC = ∠DAC and ∠BCA = ∠DCA

Prove that : AB = AD and CB = CD.

 Statements Reasons 1) ∠BAC = ∠DAC 1) Given 2) AC = AC 2) Reflexive 3) ∠BCA = ∠DCA 3) Given 4) ΔBAC ≅ ΔDAC 4) By ASA (angle side angle postulate) 5) AB = AD 5) CPCTC 6) CB = CD 6) CPCTC

2) Given : ∠BCD = ∠ADC and ∠ACB = ∠BDA

Prove that : AD = BC and ∠A = ∠B

 Statements Reasons 1) ∠BCD = ∠ADC 1) Given 2) ∠ACB = ∠BDA 2) Given 3) ∠BCD + ∠ACB = ∠ADC + ∠BDA 3) Adding (1) and (2) 4) ∠ACD = ∠BDC 4) Addition property 5) CD = CD 5) Reflexive 6) ΔACD ≅ ΔBDC 6) By ASA postulate 7) AD = BC 7) CPCTC 8) ∠A = ∠B 8) CPCTC

3) Given : AC = BC , ∠DCA = ∠ECB and ∠DBC = ∠EAC

Prove that : i) ΔDBC ≅ ΔEAC
(ii) DC = EC and (iii) BD = AE

 Statements Reasons 1) ∠DCA = ∠ECB 1) Given 2) ∠DCA + ∠ECD = ∠ECB + ∠ECD 2) Adding angle ∠ECD both sides in (1) 3) ∠ECA = ∠DCB 3) Addition property 4) BC = AC 4) Given 5) ∠DBC = ∠EAC 5) Given 6) ΔDBC ≅ ΔEAC 6) By ASA postulate 7) DC = EC 7) CPCTC 8) BD = AE 8) CPCTC

Side Angle Side Postulate
Side Side Side Postulate
Angle Angle Side Postulate
Angle Side Angle Postulate
HL postulate(Hypotenuse – Leg OR RHS)

From Angle Side Angle to Postulates of Congruent triangle

Home Page

Covid-19 has affected physical interactions between people.

Don't let it affect your learning.