Question

1. in quadrilateral rstv, rs = 5 ft, st = 2 ft, tv = 4 ft, and vr = 3 ft. in quadrilateral lnpq, np = 2 ft, pq = 4 ft, ql = 3 ft, and ln = 5 ft. is quadrilateral rstv congruent to quadrilateral lnpq?

a yes, because rs is congruent to ln.
b no, because rs is not congruent to np.
c yes, because all of their corresponding sides are congruent.
d no, because all of their corresponding angles are not congruent.

Explanation:

Step1: Check side - side correspondence

For two quadrilaterals to be congruent, all corresponding sides must be congruent.
In quadrilateral \(RSTV\), \(RS = 5\) ft, \(ST=2\) ft, \(TV = 4\) ft, \(VR = 3\) ft.
In quadrilateral \(LNPQ\), \(LN = 5\) ft, \(NP = 2\) ft, \(PQ = 4\) ft, \(QL = 3\) ft.
We check the correspondence: \(RS\) corresponds to \(LN\) (\(RS=LN = 5\) ft), \(ST\) corresponds to \(NP\) (\(ST = NP=2\) ft), \(TV\) corresponds to \(PQ\) (\(TV = PQ = 4\) ft), \(VR\) corresponds to \(QL\) (\(VR=QL = 3\) ft).

Step2: Apply the SSSS (Side - Side - Side - Side) congruence criterion for quadrilaterals

If the four sides of one quadrilateral are congruent to the four corresponding sides of another quadrilateral, then the two quadrilaterals are congruent.
Since \(RS\cong LN\), \(ST\cong NP\), \(TV\cong PQ\), \(VR\cong QL\), by the SSSS criterion, quadrilateral \(RSTV\cong\) quadrilateral \(LNPQ\)

Answer:

C. Yes, because all of their corresponding sides are congruent.