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

If ΔABC ~ ΔPQR, AB : PQ = 4 : 5 and A(ΔPQR) = 125 cm², then find A(ΔABC).

In ΔABC, seg XY || side AC. If 2AX = 3BX and XY = 9, then find the value of AC.

ΔABC ~ ΔPQR. In ΔABC, AB = 5.4 cm, BC = 4.2 cm, AC = 6.0 cm, AB:PQ = 3:2, then construct ΔABC and ΔPQR.

□ABCD is a parallelogram. Point P is the midpoint of side CD. seg BP intersects diagonal AC at point X, then prove that: 3AX = 2AC

Prove that, The areas of two triangles with the same height are in proportion to their corresponding bases. To prove this theorem start as follows:

1. Draw two triangles, give the names of all points, and show heights.
2. Write 'Given' and 'To prove' from the figure drawn.

From the information given in the figure, determine whether MP is the bisector of ∠KMN.

In the figure with ΔABC, P, Q, R are the mid-points of AB, AC and BC respectively. Then prove that the four triangles formed are congruent to each other.

If ΔABC ∼ ΔDEF such that ∠A = 92° and ∠B = 40°, then ∠F = ?

In the adjoining figure, ΔADB ∼ ΔBDC. Prove that BD² = AD × DC.

In the given figure, ΔPQR is a right-angled triangle with ∠PQR = 90°. QS is perpendicular to PR. Prove that pq = rx.

Use area theorem of similar triangles to prove congruency of two similar triangles with equal areas.

Find the length of ST, if ΔPQR ∼ ΔPST.

In the given figure, ΔLMN is similar to ΔPQR. To find the measure of ∠N, complete the following activity.

Given: ΔLMN ∼ ΔPQR

Since ΔLMN ∼ ΔPQR, therefore, corresponding angles are equal.

So, ∠L ≅ `square`

⇒ ∠L = `square`

We know, the sum of angles of a triangle = `square`

∴ ∠L + ∠M + ∠N = `square`

Substituting the values of ∠L and ∠M in equation (i),

`square` + `square` + ∠N = `square`

∠N + `square` = `square`

∠N = `square` – `square`

∠N = `square`

 Hence, the measure of ∠N is `square`.

If ΔABC ∼ ΔDEF, length of side AB is 9 cm and length of side DE is 12 cm, then find the ratio of their corresponding areas.

Construct an equilateral triangle of side 7 cm. Now, construct another triangle similar to the first triangle such that each of its sides are `5/7` times of the corresponding sides of the first triangle.

In the given figure, S is a point on side QR of ΔPQR such that ∠QPR = ∠PSR. Use this information to prove that PR² = QR × SR.

A tangent ADB is drawn to a circle at D whose centre is C. Also, PQ is a chord parallel to AB and ∠QDB = 50°. Find the value of ∠PDQ.

If the perimeter of two similar triangles is in the ratio 2 : 3, what is the ratio of their sides?

The sum of two angles of a triangle is 150°, and their difference is 30°. Find the angles.

In the figure, PQ ⊥ BC, AD ⊥ BC. To find the ratio of A(ΔPQB) and A(ΔPBC), complete the following activity.

Given: PQ ⊥ BC, AD ⊥ BC

Now, A(ΔPQB)  = `1/2 xx square xx square`

A(ΔPBC)  = `1/2 xx square xx square`

Therefore, 

`(A(ΔPQB))/(A(ΔPBC)) = (1/2 xx square xx square)/(1/2 xx square xx square)`

= `square/square`