Question

Given: PQ congruent to SR, PQR congruent to SRQ
Prove: PQR congruent to SRQ

Answer 1

ΔPQR is congruent to ΔSRQ b the Side-Angle-Side rule of congruency
`{}`

Explanation:

The two column proof is given as follows;

Statement
`{}` Reason

1.
`\overline {PQ}` ≅
`\overline {SR}`
`{}` Given

2. ∠PQR ≅ ∠SRQ
`{}` Given

3.
`\overline {QR}` ≅
`\overline {QR}`
`{}` By reflexive property

4. ΔPQR ≅ ΔSRQ
`{}` By SAS rule of congruency
`{}`

When two sides and an included angle of one triangle are congruent to the corresponding two side and an included angle of another triangle, both triangles are said to be congruent by the Side-Angle-Side SAS rule of congruency.