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In the figure, PQ is parallel to RS. The legth of RP is 4 cm; the length of PT is 16 cm; the length of QT is 20 cm. What is the length of SQ?

In the figure PQ is parallel to RS The legth of RP is 4 cm the length of PT is 16 cm the length of QT is 20 cm What is the length of SQ class=

Respuesta :

Ying22
RP/PT=SQ/QT
4/16=SQ/20
SQ=5
frika

In the figure, PQ is parallel to RS, then

  • ∠TPQ≅∠TRS (as corresponding angles);
  • ∠TQP≅∠TSR (as corresponding angles).

Consider triangles TPQ and TRS. These triangles are similar by AAA theorem, because

  • ∠TPQ≅∠TRS (as corresponding angles);
  • ∠TQP≅∠TSR (as corresponding angles);
  • ∠T is common.

Then

[tex]\dfrac{TP}{TR}=\dfrac{TQ}{TS}.[/tex]

If PR = 4 cm and PT = 16 cm, then TR = TP + PR = 16 + 4 = 20 cm.

Thus,

[tex]\dfrac{16}{20}=\dfrac{20}{TS}\Rightarrow TS=\dfrac{20\cdot 20}{16}=25\ cm.[/tex]

Note that TQ + QS = TS, then QS = TS - TQ = 25 - 20 = 5 cm.

Answer: correct choice is A

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