मराठी

In the given diagram, ΔABC ∼ ΔPQR. If AD and PS are bisectors of ∠BAC and ∠QPR respectively then ______. - Mathematics

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प्रश्न

In the given diagram, ΔABC ∼ ΔPQR. If AD and PS are bisectors of ∠BAC and ∠QPR respectively then ______.

 

पर्याय

  • ΔABC ∼ ΔPQS

  • ΔABD ∼ ΔPQS

  • ΔABD ∼ ΔPSR

  • ΔABC ∼ ΔPSR

MCQ
रिकाम्या जागा भरा

उत्तर

In the given diagram, ΔABC ∼ ΔPQR. If AD and PS are bisectors of ∠BAC and ∠QPR respectively then ΔABD ∼ ΔPQS.

Explanation:


Here, ΔABC ∼ ΔPQR

∴ ∠A = ∠P

Then, `1/2 ∠A = 1/2 ∠P` or ∠BAD = ∠QPS  ...(i)

And ∠B = ∠Q   ...(ii)

In ΔABD and ΔPQS,

∠BAD = ∠QPS  ...[From (i)]

∠B = ∠Q   ...[From (ii)]

Then, ΔABD ∼ ΔPQS   ...(By AA similarity criterion)

shaalaa.com
Conditions for Similarity of Two Triangles: (Sas, Aa Or Aaa and Sss)
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