SSC (Marathi Semi-English) 10th Standard Board Exam [इयत्ता १० वी] - Maharashtra State Board Important Questions for Geometry Mathematics 2

In the given figure 1.66, seg PQ || seg DE, A(∆PQF) = 20 units, PF = 2 DP, then Find A(◻DPQE) by completing the following activity. 

Select the appropriate alternative.
In ∆ABC and ∆PQR, in a one to one correspondence \[\frac{AB}{QR} = \frac{BC}{PR} = \frac{CA}{PQ}\] 

 In ∆ABC and ∆DEF ∠B = ∠E, ∠F = ∠C and AB = 3DE then which of the statements regarding the two triangles is true ?

In the given figure, seg XY || seg BC, then which of the following statements is true?

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

`"A(∆ ABD)"/"A(∆ ADC)"`

In the given figure, seg PA, seg QB, seg RC, and seg SD are perpendicular to line AD.

AB = 60, BC = 70, CD = 80, PS = 280 then find PQ, QR, and RS. 

In the given fig, bisectors of ∠B and ∠C of ∆ABC intersect each other in point X. Line AX intersects side BC in point Y. AB = 5, AC = 4, BC = 6 then find `"AX"/"XY"`.

In the given fig, XY || seg AC. If 2AX = 3BX and XY = 9. Complete the activity to Find the value of AC.  

Activity: 2AX = 3BX  

∴ `"AX"/"BX" = square/square`

`("AX" +"BX")/"BX" = (square + square)/square`   ...(by componendo)

`"AB"/"BX" = square/square`           ...(I)

ΔBCA ~ ΔBYX             ...`square` test of similarity,

∴ `"BA"/"BX" = "AC"/"XY"`    ...(corresponding sides of similar triangles)

∴ `square/square = "AC"/9`      

∴ AC = `square`        ...[From(I)]

In the given figure, the vertices of square DEFG are on the sides of ∆ABC. ∠A = 90°. Then prove that DE² = BD × EC. (Hint: Show that ∆GBD is similar to ∆CFE. Use GD = FE = DE.) 

Select the correct alternative answer and write it.

The ratio of corresponding sides of similar triangles is 5 : 7, then what is
the ratio of their areas ?

(A)25 : 49 (B) 49 : 25 (C) 5 : 7 (D) 7 : 5

In the given figure, CB ⊥ AB, DA ⊥ AB.
if BC = 4, AD = 8 then `(A(Δ ABC))/(A(Δ ADB))` find.

In Δ ABC and Δ PQR,
∠ ABC ≅ ∠ PQR, seg BD and
seg QS are angle bisector.
`If  (l(AD))/(l(PS)) = (l(DC))/(l(SR))`
Prove that : Δ ABC ∼ Δ PQR

In the figure, parts of the two triangles bearing identical marks are
congruent. State the test by which the triangles are congruent.

In Δ PQR, points S and T
are the midpoints of sides PQ
and PR respectively.
If ST = 6.2 then find the length of QR.

Δ ABC ∼ Δ PQR. If A(Δ ABC)=25, A(ΔPQR)=16, find AB : PQ.
(A) 25:16
(B) 4:5
(C) 16:25
(D) 5:4

In the adjoining figure,
PQ ⊥ BC, AD ⊥ BC,
PQ = 4, AD = 6
Write down the following ratios.
(i)`(A(ΔPQB))/(A(ΔADB))`

(ii)`(A(ΔPBC))/(A(ΔABC))`

Seg NQ is the bisector of ∠ N
of Δ MNP. If MN= 5, PN =7,
MQ = 2.5 then find QP.

In the adjoining figure,
seg XY || seg AC, If 3AX = 2BX
and XY = 9 then find the length of AC.

Draw an isosceles triangle with base 5 cm and height 4 cm. Draw a triangle similar to the triangle drawn whose sides are `2/3` times the sides of the triangle.

In ΔPQR, PQ = 10 cm, QR = 12cm, PR = 8 cm, find the biggest and the smallest angle of the triangle.