Exemplar Exercise 6.1 (Triangles)

 In Fig. 6.2, ∠BAC = 90° and AD ⊥ BC. Then,

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The lengths of the diagonals of a rhombus are 16 cm and 12 cm. Then, the length of the side of the rhombus is

If △ABC ~ △EDF and △ABC is not similar to △DEF, then which of the following is not true?

If in two triangles ABC and PQR, $\frac{AB}{QR}=\frac{BC}{PR}=\frac{CA}{PQ}$, then

In Fig.6.3, two line segments AC and BD intersect each other at the point P such that  PA = 6 cm, PB = 3 cm, PC = 2.5 cm, PD = 5 cm, ∠APB = 50° and ∠CDP = 30°. Then, ∠PBA is equal to

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If in two triangles DEF and PQR, ∠D = ∠Q and ∠R = ∠E, then which of the following is not true?

In triangles ABC and DEF, ∠B = ∠E, ∠F = ∠C and AB = 3 DE. Then, the two triangles are

It is given that △ABC ~ △PQR, with $\frac{BC}{QR}=\frac{1}{3}$. Then, $\frac{\mathrm{ar}\left(\mathrm{PQR}\right)}{\mathrm{ar}\left(\mathrm{BCA}\right)}$ is equal to

It is given that △ABC ~ △DFE, ∠A =30°, ∠C = 50°, AB = 5 cm, AC = 8 cm and DF = 7.5 cm. Then, the following is true:

If in triangles ABC and DEF, $\frac{\mathrm{AB}}{\mathrm{DE}}=\frac{\mathrm{BC}}{\mathrm{FD}}$, then they will be similar, when

If △ABC ~ △QRP, $\frac{\mathrm{ar}\left(\mathrm{ABC}\right)}{\mathrm{ar}\left(\mathrm{PQR}\right)}=\frac{9}{4}$, AB = 18 cm and BC = 15 cm, then PR is equal to

If S is a point on side PQ of a △PQR such that PS = QS = RS, then