Question

1. prove that triangle abd is congruent to triangle pqr.

triangle abc: ab = 7.1cm, bc = 4.8cm, ac = 6.9cm
triangle pqr: pr = 4.8cm, pq = 7.1cm, rq = 6.9cm
diagram not to scale

Explanation:

Step1: Identify Corresponding Sides

In triangle \(ABD\) (wait, actually triangle \(ABC\) as per diagram) and triangle \(PQR\):

• \(AB = 7.1\space cm\), \(PQ = 7.1\space cm\)
• \(BC = 4.8\space cm\), \(PR = 4.8\space cm\)
• \(AC = 6.9\space cm\), \(RQ = 6.9\space cm\) (assuming typo, should be \(ABD\) as \(ABC\) but problem says \(ABD\), maybe \(D\) is \(C\) typo)

Step2: Apply SSS Congruence Criterion

SSS (Side - Side - Side) congruence states that if three sides of one triangle are equal to three corresponding sides of another triangle, the triangles are congruent.
For \(\triangle ABD\) (corrected as \(\triangle ABC\)) and \(\triangle PQR\):
\(AB = PQ = 7.1\space cm\)
\(BD\) (or \(BC\)) \(= PR = 4.8\space cm\)
\(AD\) (or \(AC\)) \(= RQ = 6.9\space cm\)
By SSS congruence criterion, \(\triangle ABD\cong\triangle PQR\) (after correcting the triangle label from \(ABC\) to \(ABD\) if it's a typo).

Answer:

By the SSS (Side - Side - Side) congruence criterion, since \(AB = PQ = 7.1\space cm\), \(BD=PR = 4.8\space cm\), and \(AD = RQ=6.9\space cm\), \(\triangle ABD\cong\triangle PQR\)