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

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.

Digonals of parallelogram WXYZ intersect at point O. If OY =5, find WY.

In right angle ΔABC, if ∠B = 90°, AB = 6, BC = 8, then find AC.

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.

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

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

If the angles of a triangle are 30°, 60°, and 90°, then shown that the side opposite to 30° is half of the hypotenuse, and the side opposite to 60° is `sqrt(3)/2` times of the hypotenuse.

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.

Choose the correct alternative:

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

Choose the correct alternative:

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