Question

In the figure alongside, AD ⊥ BC, AD ⊥ EF and ∠1 = ∠4. Prove that ∆ ≅∆ ABD ACD.

Answer 1

Answer:

given = AD perpendicular to BC as well as EF

angle 1 = angle 4

To prove = Triangles ABD and ACD are congruent

proof = in triangle ABD and ACD

as AD is perpendicular to EF

it simplies that angle DAF = DAE {Each 90 degree}

so subtracting equal angles that is angle 1 and angle 2 from angle DAF and DAE

=angle 2 = angle 3. (ANGLE)

AD = AD. (COMMON SIDE)

angle ADB=angle ADC (Given)

hence both triangles are congruent by ASA congruency rule

Answer 2

Answer:

Explanatiogiven = AD perpendicular to BC as well as EF

angle 1 = angle 4

To prove = Triangles ABD and ACD are congruent

proof = in triangle ABD and ACD

as AD is perpendicular to EF

it simplies that angle DAF = DAE {Each 90 degree}

so subtracting equal angles that is angle 1 and angle 2 from angle DAF and DAE

=angle 2 = angle 3. (ANGLE)

AD = AD. (COMMON SIDE)

angle ADB=angle ADC (Given)

hence both triangles are congruent by ASA congruency rule: