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

ΔABC ∼ ΔDEF and A(ΔABC) : A Δ(DEF) = 1 : 2 If AB = 4 find DE.

With the help of the information given in the figure, fill in the boxes to find AB and BC .

AB = BC                    (Given)

∴∠ BAC = ∠ BCA =     
∴ AB = BC =    × AC
=     × `sqrt8`
=        × `2sqrt2`
= 2

From the top of a light house, an abserver looking at a boat makes an angle of depression of 600. If the height of the lighthouse is 90 m then find how far is the boat from the lighthouse. (3 = 1.73)

O is any point in the interior of ΔABC. Bisectors of ∠AOB, ∠BOC and ∠AOC intersect side AB, side BC, side AC in
F, D and E respectively.
Prove that
BF × AE × CD = AF × CE × BD

If ΔABC ~ ΔPQR  and ∠A = 60°, then ∠P = ?

In ΔABC, ray BD bisects ∠ABC.

If A – D – C, A – E – B and seg ED || side BC, then prove that:

`("AB")/("BC") = ("AE")/("EB")`

Proof : 

In ΔABC, ray BD bisects ∠ABC.

∴ `("AB")/("BC") = (......)/(......)`   ......(i) (By angle bisector theorem)

In ΔABC, seg DE || side BC

∴ `("AE")/("EB") = ("AD")/("DC")`   ....(ii) `square`

∴ `("AB")/square = square/("EB")`   [from (i) and (ii)]

In ΔABC, ∠ACB = 90°. seg CD ⊥ side AB and seg CE is angle bisector of ∠ACB.

Prove that: `(AD)/(BD) = (AE^2)/(BE^2)`.

In the following figure, in Δ PQR, seg RS is the bisector of ∠PRQ.

PS = 11, SQ = 12, PR = 22. Find QR.

The ratio of the areas of two triangles with the common base is 4 : 3. Height of the larger triangle is 2 cm, then find the corresponding height of the smaller triangle.

In ∆ABC, B – D – C and BD = 7, BC = 20, then find the following ratio.

`(A(∆ABD))/(A(∆ABC))`

In the given, seg BE ⊥ seg AB and seg BA ⊥ seg AD.

if BE = 6 and AD = 9 find `(A(Δ ABE))/(A(Δ BAD))`.

In the figure, ray YM is the bisector of ∠XYZ, where seg XY ≅ seg YZ, find the relation between XM and MZ. 

In the above figure, line l || line m and line n is a transversal. Using the given information find the value of x. 

Draw seg AB = 6.8 cm and draw perpendicular bisector of it. 

If ΔABC ~ ΔDEF, then writes the corresponding congruent angles and also write the ratio of corresponding sides. 

Choose the correct alternative: 
If ΔABC ~ ΔPQR and 4A (ΔABC) = 25 A(ΔPQR), then AB : PQ = ? 

In the above figure, line AB || line CD || line EF, line l, and line m are its transversals. If  AC = 6, CE = 9. BD = 8, then complete the following activity to find DF. 

Activity :

`"AC"/"" = ""/"DF"`   (Property of three parallel lines and their transversal) 

∴ `6/9 = ""/"DF"`

∴ `"DF"  = "___"`

In the following figure, state whether the triangles are similar. Give reason.

In the following figure, ray PT is the bisector of ∠QPR Find the value of x and perimeter of ∠QPR.

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