Question

In triangle ABC and triangle DEF ,AB =4 CM ,DE=4 CM, m angle A=70 degree , m angle D=70 degree, m angle B=50 degree, m angle E=50 degree. Prove that triangle ABC and triangle DEF are congruent

Answer 1

angle A = angle D... given

angle B = angle E...given

side AB = side DE ...given

..° therefore , triangle ABC is congruent to triangle DEF ...by AAS test.

Answer 2

Answer:

Sol. In triangle ABC and triangle DEF

m∠A = m∠D = 70° (Given)

AB = DE = 4cm (Given)

m∠B = m∠E = 50° (Given)

Then  ABC ≅  DEF (By A-S-A Congruency)

Q.2 AB and CD are line segments which intersect at E, BA bisects

CD, AC ⊥ CD, BD ⊥ CD. Prove that  ACE ≅  BDE.

Sol. In triangle ACE and triangle BDE

m∠C = m∠D = 90° (Given)

CE = DE (Given, BA bisects CD)m∠CEA = m∠DEB (Vertically opposite angle)

Then  ACE ≅  BDE (By A-S-A Congruency)