Question

ABCD is a parallalogram and AC is one of its diagonals. Prove that AABC = AACD.​

Answer 1

Step-by-step explanation:

Given:

ABCD is a parallalogram and AC is one of its diagonals.

To Prove:

∆ABC ≅ ∆ACD

Note: Split the Quadrilateral in two triangles ∆ABC and ∆ACD!

Proof:

In ∆ABC and ∆ACD we have,

AC = AC ----- [Common Side]

∠ABC = ∠ADC ------ [Each 90°]

∠BAC = ∠ACD ------ [Alternate Angles of triangle are equal]

So, By AAS Congruence Condition ∆ABC ≅ ∆ACD ------ { Equation 1}

Hence from { Equation 1 } ∆ABC ≅ ∆ACD

⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

Symbol Language:

∆ = Triangle

≅ = Congruent Symbol

AAS = Angle Angle Side Congruence Condition.