SSC (English Medium) इयत्ता १० वी - Maharashtra State Board Question Bank Solutions for Geometry Mathematics 2

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

Prove that “That ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding sides.”

Circles with centres A, B and C touch each other externally. If AB = 3 cm, BC = 3 cm, CA = 4 cm, then find the radii of each circle.

Which of the following is not a test of similarity?

Given ΔABC ~ ΔDEF, if ∠A = 45° and ∠E = 35° then ∠B = ?

If ΔABC ~ ΔLMN and ∠A = 60° then ∠L = ?

In ΔDEF and ΔXYZ, `"DE"/"XY" = "FE"/"YZ"` and ∠E ≅ ∠Y. _______ test gives similarity between ΔDEF and ΔXYZ.

Are triangles in figure similar? If yes, then write the test of similarity.

State whether the following triangles are similar or not: If yes, then write the test of similarity.

∠P = 35°, ∠X = 35° and ∠Q = 60°, ∠Y = 60°

If ΔABC ~ ΔLMN and ∠B = 40°, then ∠M = ? Give reason.

ΔPQR ~ ΔSUV. Write pairs of congruent angles

ΔABC ~ ΔDEF. Write the ratios of their corresponding sides

Write the test of similarity for triangles given in figure.

In fig. BP ⊥ AC, CQ ⊥ AB, A−P−C, and A−Q−B then show that ΔAPB and ΔAQC are similar.

In ΔAPB and ΔAQC

∠APB = [   ]°     ......(i)

∠AQC = [   ]°  ......(ii)

∠APB ≅ ∠AQC    .....[From (i) and (ii)]

∠PAB ≅ ∠QAC    .....[______]

ΔAPB ~ ΔAQC     .....[______]

Observe the figure and complete the following activity

In fig, ∠B = 75°, ∠D = 75°

∠B ≅ [ ______ ]       ...[each of 75°]

∠C ≅ ∠C         ...[ ______ ]

ΔABC ~ Δ [ ______ ]     ...[ ______ similarity test]

ΔABC ~ ΔPQR, A(ΔABC) = 80 sq.cm, A(ΔPQR) = 125 sq.cm, then complete `("A"(Δ"ABC"))/("A"(Δ"PQR")) = 80/125 = (["______"])/(["______"])`, hence `"AB"/"PQ" = (["______"])/(["______"])`

In fig., seg AC and seg BD intersect each other at point P.

`"AP"/"PC" = "BP"/"PD"` then prove that ΔABP ~ ΔCDP

ΔABP ~ ΔDEF and A(ΔABP) : A(ΔDEF) = 144:81, then AB : DE = ?

Areas of two similar triangles are 225 cm² and 81 cm². If side of smaller triangle is 12 cm, find corresponding side of major triangle. 

In ΔABC, AP ⊥ BC and BQ ⊥ AC, B−P−C, A−Q−C, then show that ΔCPA ~ ΔCQB. If AP = 7, BQ = 8, BC = 12, then AC = ?

In ΔCPA and ΔCQB

∠CPA ≅ [∠ ______]    ...[each 90°]

∠ACP ≅ [∠ ______]   ...[common angle]

ΔCPA ~ ΔCQB     ......[______ similarity test]

`"AP"/"BQ" = (["______"])/"BC"`    .......[corresponding sides of similar triangles]

`7/8 = (["______"])/12`

AC × [______] = 7 × 12

AC = 10.5