SOLUTION: 1. Suppose that square PQRS has 15-cm sides, and that
G and H are on QR and PQ, respectively, so that PH and
QG are both 8 cm long. Let T be the point where PG
meets SH. Find
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-> SOLUTION: 1. Suppose that square PQRS has 15-cm sides, and that
G and H are on QR and PQ, respectively, so that PH and
QG are both 8 cm long. Let T be the point where PG
meets SH. Find
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Question 1072247: 1. Suppose that square PQRS has 15-cm sides, and that
G and H are on QR and PQ, respectively, so that PH and
QG are both 8 cm long. Let T be the point where PG
meets SH. Find the size of angle STG, with justification.
Find the lengths of PG and PT. Answer by Edwin McCravy(20064) (Show Source):
You can put this solution on YOUR website! 1. Suppose that square PQRS has 15-cm sides, and that
G and H are on QR and PQ, respectively, so that PH and
QG are both 8 cm long. Let T be the point where PG
meets SH. Find the size of angle STG, with justification.
Find the lengths of PG and PT.
ΔHPS≅ΔGQP because they are right triangles with legs
HP = 8 = GQ, QP = 15 = PS, ∠GQP = ∠HPS = 90° because
PQRS is a square.
ΔHTP∽ΔHPS because the pair of acute angles of ΔHTP are
the same pair of acute angles in ΔHPS and ΔGQP.
∠HTP = 90° by similar triangles, and so
∠STG = 90°
because it and ∠HTP are vertical (opposite) angles.
PG = 17 because by the Pythagorean theorem,
PG2 = PQ2 + QG2 = 152 + 82 = 225 + 64 = 289
PG = √289 = 17
By similar triangles
cm.
Edwin
