Item 3
2 answers:
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Answer:
(B)
Step-by-step explanation:
It is given that: From ΔONP and ΔMLP,
(By basic proportionality theorem)
∠MPL=LPM(Common)
Therefore, ΔONP is similar to ΔMLP by SAS similarity postulate.
Also, From ΔONP and ΔKPJ,
(By basic proportionality theorem)
∠OPN=KPJ(Common)
therefore, ΔONP is similar to ΔKPJ by SAS similarity postulate.
Now, since ΔONP is similar to ΔMLP by SAS similarity postulate and ΔONP is similar to ΔPJK by SAS similarity postulate, therefore ΔMLP is similar to ΔPJK by SAS similarity postulate.
Thus, all the three center triangles are similar by SSS similarity postulate.