Question

three figures exist such that abcd ≅ ghij and bcda ≅ rstu. if gh = 6 cm, hi = 8 cm, ij = 10 cm, and gj = 9 cm, what is ts?

Explanation:

Step1: Understand congruent figures

Congruent figures have equal - corresponding sides. Since \(ABCD\cong GHIJ\) and \(BCDA\cong RSTU\), the figures \(GHIJ\) and \(RSTU\) are congruent (by the transitive property of congruence as they are both congruent to related figures).

Step2: Identify corresponding sides

In congruent figures, corresponding sides are equal. The order of the vertices matters. If we consider the congruence of the figures, the side \(TS\) in figure \(RSTU\) corresponds to the side \(HI\) in figure \(GHIJ\).

Step3: Find the length of \(TS\)

Given \(HI = 8\mathrm{cm}\), and since \(TS=HI\) (corresponding sides of congruent figures), then \(TS = 8\mathrm{cm}\).

Answer:

8 cm