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musickatia [10]
3 years ago
5

Show that the two triangles given beside are similar and calculate the lengths of sides PQ and PR.

Mathematics
1 answer:
Rina8888 [55]3 years ago
5 0

9514 1404 393

Answer:

  • ΔABC ~ ΔPQR
  • PQ = 8
  • PR = 14

Step-by-step explanation:

Angles A and P are marked congruent; angles B and Q are marked congruent, so the triangles are similar by the AA similarity postulate. The similarity statement can be written ...

  ΔABC ~ ΔPQR by AA similarity

__

The ratio of sides of PQR to ABC is the ratio QR/BC = 12/6 = 2. That is, each side in the larger triangle is 2 times the length of the corresponding smaller side.

  PQ = 2·AB = 2·4 = 8

  PR = 2·AC = 2·7 = 14

The side lengths of interest are ...

  PQ = 8, PR = 14

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