Question

In the given figure, l || m
(i) Name three pairs of similar triangles with proper correspondence; write similarities.
(ii) Prove that $\frac {AB}{PQ} =\frac {AC}{PR} =\frac {BC}{RQ}$

Answer 1

Answer:

The three pairs of similar triangles with proper correspondence are ∆AKB ~ ∆PQK , ∆CBK ~ ∆RQK & ∆ACK ~ ∆PRK  and it is  Proved that AB/PQ = AC/PR = BC/RQ

Step-by-step explanation:

(i) The three pairs of similar triangles with proper correspondence are :  

(1) In ∆AKB & ∆PQK

∠BAK = ∠QPK  (alternate interior angles)

∠AKB = ∠PKQ  (vertically opposite angles)

∆AKB ~ ∆PQK   [By AA similarity]

AB/PQ = AK/PK = BK/QK ………….(1)

[Corresponding sides of similar triangles are proportional]

(2) In  ∆CBK & ∆RQK

∠BCK = ∠QRK  (alternate interior angles)

∠BKC = ∠QKR  (vertically opposite angles)

∆CBK ~ ∆RQK   [By AA similarity]

CB/RQ = CK/RK = BK/QK ………….(2)

[Corresponding sides of similar triangles are proportional]

(3) In  ∆ACK & ∆PRK

∠KAC = ∠KPR  (alternate interior angles)

∠KCA = ∠KRP  (alternate interior angles)

∆ACK ~ ∆PRK  [By AA similarity]

AC/PR = AK/PK = CK/RK ………….(3)

[Corresponding sides of similar triangles are proportional]

(ii) On comparing equation 1 , 2 and 3

AB/PQ = AC/PR = BC/RQ  

Hence, the three pairs of similar triangles with proper correspondence are ∆AKB ~ ∆PQK , ∆CBK ~ ∆RQK & ∆ACK ~ ∆PRK , and it is Proved that AB/PQ = AC/PR = BC/RQ  

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Answer 2

Step-by-step explanation:

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