If \(\triangle ABC\sim \triangle DFE\), \(\angle A={ 30 }^{ ° }\) , \(\angle C={ 50 }^{ ° }\) , AB = 5 cm, AC = 8 cm and DF = 75 cm, then find DE and \(\angle F\)

5

(a)

If the areas of two similar triangles are respectively 81 cm² and 49 cm²  Find the ratio of their corresponding medians.

5

(a)

If the lengths of the diagonals of rhombus are 16 cm and 12 cm. Then, find the length of the sides of the rhombus.

5

(a)

E and F are points on the sides PQ and PR respectively of a ΔPQR. For the following case, state whether EF || QR. PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm

5

(a)

A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut?

5

(a)

Shweta prepared two posters on National Integration for decoration on Independence day on triangular sheets (say ABC and DEF). The sides AB and AC and the perimeter P₁ of \(\triangle ABC\) are respectively four times the corresponding sides DE and DF and the perimeter P₂ of \(\triangle DEF\). Are the two triangular sheets similar? If yes, find \(\frac { ar\left( \triangle ABC \right) }{ ar\left( \triangle DEF \right) } \). What values can be indicated through celebration of national festivals?

5

(a)

\(\triangle ABC\) and \(\triangle AMP\) are two right angled triangles. right angled at B and M, respectively. Prove that CA x MP = PA x BC

5

(a)

ABCD is a trapezium with \(AB\parallel DC\). If \(\triangle AED\sim \triangle BEC\), then prove that AD = BC.

5

(a)

In the given figure, if \(\angle BAC\) = 90° and \(AD\bot BC\) . prove thart AD² = BD.CD

5

(a)

In the given figure, \(DE\parallel BC\) . DE = 4 cm, BC = 8 cm, area of \(\triangle ADE\) = 25 sq.cm. Find the area of \(\triangle ABC\)

5

(a)

Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of any equilateral triangle described on one its diagonals.

5

(a)

In the given figure, if CD = 17 m, BD = 8 m and AD = 4 m, find the value of AC.

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(a)