SSC (English Medium) १० वीं कक्षा - Maharashtra State Board Important Questions

In ΔDEF, if ∠E = 90°, then find the value of ∠D + ∠F. 

Choose the correct alternative: 

In right-angled triangle PQR, if hypotenuse PR = 12 and PQ = 6, then what is the measure of ∠P? 

Find the side and perimeter of a square whose diagonal is `13sqrt2` cm. 

In ΔABC, seg AP is a median. If BC = 18, AB² + AC² = 260, then find the length of AP. 

Find the length of diagonal of the square whose side is 8 cm.

Find the side of the square whose diagonal is `16sqrt(2)` cm.

Out of given triplets, which is not a Pythagoras triplet?

If length of sides of a triangle are a, b, c and a² + b² = c², then which type of triangle it is?

From given figure, In ∆ABC, AB ⊥ BC, AB = BC 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

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

From the given figure, In ∆ABC, If AD ⊥ BC, ∠C = 45°, AC = `8sqrt(2)`, BD = 5, then for finding value of AD and BC, complete the following activity.

Activity: In ∆ADC, If ∠ADC = 90°, ∠C = 45°   ...(Given)

∴ ∠DAC = `square`   ...(Remaining angle of ∆ADC)

By theorem of 45° – 45° – 90° triangle,

∴ `square = 1/sqrt(2)` AC and `square = 1/sqrt(2)` AC

∴ AD =`1/sqrt(2) xx square` and DC = `1/sqrt(2) xx 8sqrt(2)`

∴ AD = 8 and DC = 8

∴ BC = BD + DC

= 5 + 8

= 13

Complete the following activity to find the length of hypotenuse of right angled triangle, if sides of right angle are 9 cm and 12 cm.

Activity: In ∆PQR, m∠PQR = 90°

By Pythagoras Theorem,

PQ² + `square` = PR²   ...(I)

∴ PR² = 9² + 12² 

∴ PR² = `square` + 144

∴ PR² = `square`

∴ PR = 15

∴ Length of hypotenuse of triangle PQR is `square` cm.

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.

A congruent side of an isosceles right angled triangle is 7 cm, Find its perimeter.

As shown in figure, LK = `6sqrt(2)` then (1) MK = ? (2) ML = ? (3) MN = ?

In ΔABC, ∠ABC = 90°, ∠BAC = ∠BCA = 45°. If AC = `9sqrt(2)`, then find the value of AB.

In the above figure `square`ABCD is a rectangle. If AB = 5, AC = 13, then complete the following activity to find BC.

Activity: ΔABC is a `square` triangle.

∴ By Pythagoras theorem

AB² + BC² = AC²

∴ 25 + BC² = `square`

∴ BC² = `square`

∴ BC = `square`

In ΔABC, AB = 9 cm, BC = 40 cm, AC = 41 cm. State whether ΔABC is a right-angled triangle or not. Write reason.

If a and b are natural numbers and a > b If (a² + b²), (a² – b²) and 2ab are the sides of the triangle, then prove that the triangle is right-angled. Find out two Pythagorean triplets by taking suitable values of a and b.