Question

3. In the fig. AD = DC and AB = BC. Prove that ΔADB = ΔCDB
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Answer 1

The two column proof is presented as follows;

The given parameters are;

`\overline {AD}` =
`\overline {DC}` and
`\overline {AB}` =
`\overline {BC}`

Statement
`{}` Reason

`\overline {AD}` =
`\overline {DC}` and
`\overline {AB}` =
`\overline {BC}`
`{}` Given

`\overline {BD}` ≅
`\overline {BD}`
`{}` Reflexive property

`\overline {BD}` =
`\overline {BD}`
`{}` By the definition of congruency

ΔADB ≅ ΔCDB
`{}` By Side-Side-Side (SSS) rule of congruency

ΔADB = ΔCDB
`{}` By the definition of congruency

If the three sides of one triangle are congruent to the corresponding three sides of another triangle, then both triangles are said to be congruent according to the SSS rule of congruency

Explanation: