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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