SSC (English Medium) १० वीं कक्षा - Maharashtra State Board Question Bank Solutions for Geometry Mathematics 2

Prove the following.

\[\frac{\tan\theta}{\sec\theta + 1} = \frac{\sec\theta - 1}{\tan\theta}\]

Prove the following.

In the adjoining figure, point O is the centre of the cirlcle, seg OM ⊥ chord AB. If OM = 8cm, AB = 12 cm, then find OB.

In ∆PQR, PQ = √8 , QR = √5 , PR = √3. Is ∆PQR a right-angled triangle? If yes, which angle is of 90°?

Sides of the triangle are 7 cm, 24 cm, and 25 cm. Determine whether the triangle is a right-angled triangle or not. 

Choose the correct alternative: 
sinθ × cosecθ =?

If the length of an arc of the sector of a circle is 20 cm and if the radius is 7 cm, find the area of the sector. 

If sinθ = `8/17`, where θ is an acute angle, find the value of cos θ by using identities.

Show that: 

`sqrt((1-cos"A")/(1+cos"A"))=cos"ecA - cotA"`

In ΔPQR, ∠P = 30°, ∠Q = 60°, ∠R = 90° and PQ = 12 cm, then find PR and QR.

ΔAMT∼ΔAHE, construct Δ AMT such that MA = 6.3 cm, ∠MAT=120°, AT = 4.9 cm and `"MA"/"HA"=7/5`, then construct ΔAHE.

Choose the correct alternative:

In right angled triangle, if sum of the squares of the sides of right angle is 169, then what is the length of the hypotenuse?

Choose the correct alternative:

A rectangle having length of a side is 12 and length of diagonal is 20, then what is length of other side?

Choose the correct alternative:

If the length of diagonal of square is √2, then what is the length of each side?

Choose the correct alternative:

If length of both diagonals of rhombus are 60 and 80, then what is the length of side?

Choose the correct alternative:

In ∆ABC, AB = `6sqrt(3)` cm, AC = 12 cm, and BC = 6 cm, then m∠A = ?

If a triangle having sides 50 cm, 14 cm and 48 cm, then state whether given triangle is right angled triangle or not

If a triangle having sides 8 cm, 15 cm and 17 cm, then state whether given triangle is right angled triangle or not

A rectangle having dimensions 35 m × 12 m, then what is the length of its diagonal?

In ∆LMN, l = 5, m = 13, n = 12 then complete the activity to show that whether the given triangle is right angled triangle or not.
*(l, m, n are opposite sides of ∠L, ∠M, ∠N respectively)

Activity: In ∆LMN, l = 5, m = 13, n = `square`

∴ l² = `square`, m² = 169, n² = 144.

∴ l² + n² = 25 + 144 = `square`

∴ `square` + l² = m²

∴By Converse of Pythagoras theorem, ∆LMN is right angled triangle.