Q6 of 70 Page 140

Fill in the blanks so that the following statements are true:

D, E, F are respectively the mid-points of , , of ΔPQR. The correspondence DEF ↔ _____ is similarity.

We have



Given: D is the midpoint of PQ ⇒ PD = DQ = 1/2 PQ


But PD = DQ = FE [∵, F and E are also midpoints of PR and QR respectively]


So, EF = 1/2 PQ


Or …(i)


E is the midpoint of QR ⇒ QE = ER = 1/2 RQ


But QE = ER = DF [∵, D and F are also midpoints of PQ and PR respectively]


So, DF = 1/2 RQ


Or …(ii)


F is the midpoint of PR ⇒ PF = FR = 1/2 RP


But PF = FR = DE [∵, D and E are midpoints of PQ and QR respectively]


So, DE = 1/2 RP


Or …(iii)


Comparing equations (i), (ii) & (iii), we get



We can also arrange it as,



∴ The correspondence DEF ↔ RPQ is a similarity by SSS theorem.


Thus, answer is RPQ.


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Explain with reasons, whether the following statements are true or false:

(1) AAA criterion of similarity of triangles cannot be the criterion for congruence of triangles.


(2) SAS criterion for congruence of triangles cannot be a criterion for similarity of triangles.


(3) Two congruent triangles have the same area.


(4) Two similar triangles always have the same area.


(5) Area of similar triangles are proportional to the squares of measures of their corresponding angles.

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Fill in the blanks so that the following statements are true:

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Fill in the blanks so that the following statements are true:

Areas of two similar triangles are 25 and 16. The ratio of the perimeters of the triangles is _______.