SSC (Marathi Semi-English) इयत्ता १० वी - Maharashtra State Board Important Questions for Geometry Mathematics 2

∆ABC is an equilateral triangle. Point P is on base BC such that PC = `1/3`BC, if AB = 6 cm find AP.

Find the length of the hypotenuse in a right angled triangle where the sum
of the squares of the sides making right angle is 169.
(A)15 (B) 13 (C) 5 (D) 12

Prove that, in a right angled triangle, the square of the hypotenuse is
equal to the sum of the squares of remaining two sides.

If hypotenuse of a right angled triangle is 5 cm, find the radius of
the circle passing through all vertices of the triangle.

In right angled triangle PQR,
if ∠ Q = 90°, PR = 5,
QR = 4 then find PQ and hence find tan R.

In right-angled triangle PQR, if ∠P = 60°, ∠R = 30° and PR = 12, then find the values of PQ and QR. 

Choose the correct alternative: 

ΔABC and ΔDEF are equilateral triangles. If ar(ΔABC): ar(ΔDEF) = 1 : 2 and AB = 4, then what is the length of DE?

Choose the correct alternative: 

Out of the following which is a Pythagorean triplet? 

In right-angled ΔABC, BD ⊥ AC. If AD= 4, DC= 9, then find BD.

In ΔPQR, seg PM is the median. If PM = 9, PQ² + PR² = 290, Find QR. 

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

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. 

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

From given figure, In ∆ABC, AB ⊥ BC, AB = BC then m∠A = ?

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.

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.