Pythagoras Theorem Questions & Answers: 10th (SSC) Mathematics Part 2 (Geometry), Maharashtra Board

Maharashtra SSC Geometry (Mathematics Part II) Board Paper June 2026

Full paper →

Q.1 (A)(i) Out of the following which is a Pythagorean triplet ?

1 mark · See worked answer →
Q.1 (B)(i) Find the diagonal of square whose side is 5 cm.

1 mark · See worked answer →
Q.2 (B)(ii) Find the length of diagonal of a rectangle whose length is 35 cm and breadth is 12 cm.

2 marks · See worked answer →
Q.3 (B)(i) In $\Delta PQR$, point S is the midpoint of side QR. If PQ = 11, PR = 17, PS = 13, find QR.

3 marks · See worked answer →

Full paper →

Q.1 (A)(1) Out of the following which is the Pythagorean triplet ?

1 mark · See worked answer →
Q.1 (B)(2) Find the side of a square if its diagonal is $10\sqrt{2}$ cm.

1 mark · See worked answer →
Q.2 (B)(2) In Δ RST, ∠S = 90º, ∠T = 30º, RT = 12 cm, then find RS and ST.

2 marks · See worked answer →
Q.3 (A)(2) For finding AB and BC with the help of information given in the following figure, complete the following activity :
$Figure: Δ ABC with ∠B = 90º; the sides AB and BC carry identical tick marks showing AB = BC, and the hypotenuse AC = $\sqrt{8}$.$
Activity :
AB = BC .................... ____
∴ ∠BAC = ____
∴ AB = BC = ____ × AC
= $\dfrac{1}{\sqrt{2}} \times$ ____
= $\dfrac{1}{\sqrt{2}} \times 2 \times$ ____
AB = BC = ____

3 marks · See worked answer →

Full paper →

Q.1 (A)(1) Out of the following which is a Pythagorean triplet ?

1 mark · See worked answer →
Q.1 (B)(2) In the following figure ∠MNP = 90º, seg NQ ⊥ seg MP, MQ = 9, QP = 4, find NQ.

1 mark · See worked answer →
Q.2 (B)(2) In the figure given below, find RS and PS using the information given in Δ PSR.

2 marks · See worked answer →
Q.3 (A)(2) Complete the following activity to prove that the sum of squares of diagonals of a rhombus is equal to the sum of the squares of the sides.
Given : PQRS is a rhombus. Diagonals PR and SQ intersect each other at point T.
To prove : PS² + SR² + QR² + PQ² = PR² + QS²
Activity :
Diagonals of a rhombus bisect each other.
In Δ PQS, PT is the median and in Δ QRS, RT is the median.
∴ by Apollonius theorem,
PQ² + PS² = ____ + 2QT² ................. (I)
QR² + SR² = ____ + 2QT² ................. (II)
adding (I) and (II),
PQ² + PS² + QR² + SR² = 2 (PT² + ____) + 4QT²
= 2 (PT² + ____) + 4QT² .............. (RT = PT)
= 4PT² + 4QT²
= (____)² + (2QT)²
∴ PQ² + PS² + QR² + SR² = PR² + ____ .

3 marks · See worked answer →
Q.5 (1) ABCD is a rectangle. Taking AD as a diameter, a semicircle AXD is drawn which intersects the diagonal BD at X. If AB = 12 cm, AD = 9 cm, then find the values of BD and BX.

3 marks · See worked answer →

Full paper →

Q.1 (B)(1) Find the diagonal of square whose side is 10 cm.

1 mark · See worked answer →
Q.3 (B)(4) Prove that, ‘In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of remaining two sides’.

3 marks · See worked answer →
Q.5 (1) Draw right-angled $\Delta ABC$ of lengths of sides are 3 cm, 4 cm and 5 cm. Draw median on the hypotenuse of $\Delta ABC$. Then :
(i) Measure the length of median and write it.
(ii) By observing lengths of median and hypotenuse write your observations.

3 marks · See worked answer →

Full paper →

Q.2 (B)(4) In the above figure, $\angle PQR = 90^\circ$, seg QN $\perp$ seg PR, PN = 9, NR = 16, find QN.
$Figure: right-angled $\Delta PQR$ with the right angle at Q; N lies on hypotenuse PR and seg QN is drawn perpendicular to PR, with PN = 9 and NR = 16.$

2 marks · See worked answer →
Q.4 (1) $\Delta ABC$ is an equilateral triangle. Point D is on seg BC such that BD $= \dfrac{1}{5}$ BC. Then prove that $\dfrac{AD^2}{AB^2} = \dfrac{21}{25}$.

4 marks · See worked answer →

Full paper →

Q.1 (A)(1) Out of the dates given below which date constitutes a Pythagorean triplet ?

1 mark · See worked answer →
Q.1 (B)(3) Find the side of a square whose diagonal is $10\sqrt{2}$ cm.

1 mark · See worked answer →
Q.2 (B)(2) Find the length of the hypotenuse of a right-angled triangle if remaining sides are 9 cm and 12 cm.

2 marks · See worked answer →
Q.3 (B)(3) Seg PM is a median of $\Delta PQR$, PM = 9 and PQ² + PR² = 290, then find QR.

3 marks · See worked answer →