10th Exemplar ch-6 to 11 excluding constructions

In Fig. 6.2, if BAC = 90° and AD ⊥ BC, then

• BD² . CD² = BC²
• AB² . AC² = BC²
• BD² . CD² = AD²
• AB² . AC² = AD²

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

• 9 cm
• 10 cm
• 8 cm
• 20 cm

If ΔABC ~ ΔEDF and ΔABC is not similar to ΔDEF, then which of the following is not true?

• BC . EF = AC . FD
• AB . EF = AC . DE
• BC . DE = AB . EF
• BC . DE = AB . FD

If in two triangles ABC and PQR, AB/QR = BC/PR = CA/PQ, then

• ΔPQR ~ ΔCAB
• ΔPQR ~ ΔABC
• ΔCBA ~ ΔPQR
• ΔBCA ~ ΔPQR

In Fig. , 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

• 50°
• 30°
• 60°
• 100°

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

• EF/DF = PR/PQ
• DE/EF = PQ/RP
• DE/DF = QR/PQ
• EF/DE = RP/QR

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

• congruent but not similar
• similar but not congruent
• neither congruent nor similar
• congruent as well as similar

It is given that ΔABC ~ ΔPQR, with BC/QR = 1/3. Then, ar(PRQ)/ar(BCA) is equal to

• 9
• 3
• 1/3

• 1/9

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

• DE = 12 cm, ∠F = 50°
• DE = 12 cm, ∠F = 100°
• EF = 12 cm, ∠D = 100°
• EF = 12 cm, ∠D = 30°

• ∠B = ∠E
• ∠A = ∠D
• ∠B = ∠D
• ∠A = ∠F