Question

In the following pairs of triangles of figure, the lengths of the sides are indicated along the sides. By applying SSS congruence criterion, determine which triangles are congruent. If congruent, write the results in symbolic form.

Answer 1

In ∆STU, By Pythagoras theorem,

TU² = (10.5)² – 5² = 135.25

And in ∆PQR, QR² = (10.5)² – 5² = 135.25

∴ TU² = QR² ⇒ TU = QR  ...(i)

In ∆STU and ∆PQR,

ST = PQ = 5 cm  ...(Given)

SU = PR = 10.5 cm  ...(Given)

TU = QR  ...(From (1)

∆STU ≅ ∆PQR  ...(SSS criterion)