Question

Given: AB = BC and D is the midpoint of AC.Prove: AABD - ACBD.StepStatementReason1ABBCD is the midpoint of ACGiventryType of Statement

Answer 1

Δ ABD is proved to be a congruent to Δ CBD using SSS congruence theorem

How to complete the proof

The two column proof is written as follows

Statement Reason

AB ≅ BC; given

AD ≅ DC Definition of midpoint

BD ≅ BD Transitive property

Δ ABD ≅ Δ CBD SSS congruence theorem

Answer 2

First draw the diagram.

The two triangles are drawn as, ABD and CBD.

To prove,

`\Delta ABD\cong\Delta CBD`

Proof

`AB\cong BC\text{ }(given)`
`AD=CD\text{ }(D\text{ is the midpoint})`
`\angle ABD=\angle CBD\text{ }(common)`

Thus the triangle ABD is congruent to triangle CBD by Side angle Side property.