SSC (English Medium) 10th Standard - Maharashtra State Board Important Questions for Geometry Mathematics 2

In the following figure RP : PK= 3 : 2, then find the value of A(ΔTRP) : A(ΔTPK).

ΔSHR ~ ΔSVU. In ΔSHR, SH = 4.5 cm, HR = 5.2 cm, SR = 5.8 cm and `"SH"/("SV")=3/5`. Construct ΔSVU.

Determine whether the points are collinear.

A(1, −3), B(2, −5), C(−4, 7)

Using Euler’s formula, find V if E = 30, F = 12.

In the following figure seg AB ⊥ seg BC, seg DC ⊥ seg BC. If AB = 2 and DC = 3, find `(A(triangleABC))/(A(triangleDCB))`

In the given figure, AD is the bisector of the exterior ∠A of ∆ABC. Seg AD intersects the side BC produced in D. Prove that:

\[\frac{BD}{CD} = \frac{AB}{AC}\]

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

Find the height of an equilateral triangle whose side is 6 units.

In the given figure, ∠MNP = 90°, seg NQ ⊥ seg MP, MQ = 9, QP = 4, find NQ.

Out of the following, which is the Pythagorean triplet?

Some question and their alternative answer are given.

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

Some question and their alternative answer are given. Select the correct alternative.

If a, b, and c are sides of a triangle and a² + b² = c², name the type of triangle.

Find the perimeter of a square if its diagonal is `10sqrt2` cm:

In ΔMNP, ∠MNP = 90˚, seg NQ ⊥ seg MP, MQ = 9, QP = 4, find NQ.

In ΔPQR, seg PM is a median, PM = 9 and PQ² + PR²  = 290. Find the length of QR. 

Draw ∠ABC of measure 105° and bisect it.

Write down the equation of a line whose slope is 3/2 and which passes through point P, where P divides the line segment AB joining A(-2, 6) and B(3, -4) in the ratio 2 : 3.

ΔRST ~ ΔUAY, In ΔRST, RS = 6 cm, ∠S = 50°, ST = 7.5 cm. The corresponding sides of ΔRST and ΔUAY are in the ratio 5 : 4. Construct ΔUAY.

Construct the circumcircle and incircle of an equilateral ∆XYZ with side 6.5 cm and centre O. Find the ratio of the radii of incircle and circumcircle.