SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board chapter 1 - Similarity [Latest edition]

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SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board chapter 1 - Similarity - Shaalaa.com
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Solutions for Chapter 1: Similarity

Below listed, you can find solutions for Chapter 1 of Maharashtra State Board SCERT Maharashtra Question Bank for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board.


Q.1 (A)Q.1 (B)Q.2 (A)Q.2 (B)Q.3 (A)Q.3 (B)Q.4Q.5
Q.1 (A)

SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board Chapter 1 Similarity Q.1 (A)

MCQ [1 Mark]

Q.1 (A) | Q 1

If ∆ABC ~ ∆PQR and AB : PQ = 3 : 4 then A(∆ABC) : A(∆PQR) = ?

  • 9 : 25

  • 9 : 16

  • 16 : 9

  • 25 : 9

Q.1 (A) | Q 2

Which of the following is not a test of similarity?

  • AAA

  • SAS

  • SAA

  • SSS

Q.1 (A) | Q 3

If ∆XYZ ~ ∆PQR and A(∆XYZ) = 25 cm2, A(∆PQR) = 4 cm2 then XY : PQ = ?

  • 4 : 25

  • 2 : 5

  • 5 : 2

  • 25 : 4

Q.1 (A) | Q 4

Ratio of areas of two similar triangles is 9 : 25. _______ is the ratio of their corresponding sides.

  • 3 : 4

  • 3 : 5

  • 5 : 3

  • 25 : 81

Q.1 (A) | Q 5

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

  • 45°

  • 35°

  • 25°

  • 40°

Q.1 (A) | Q 6

In fig, seg DE || sec BC, identify the correct statement.

  • `"AD"/"DB" = "AE"/"AC"`

  • `"AD"/"DB" = "AB"/"AC"`

  • `"AD"/"DB" = "EC"/"AC"`

  • `"AD"/"DB" = "AE"/"EC"`

Q.1 (A) | Q 7

If ΔXYZ ~ ΔPQR then `"XY"/"PQ" = "YZ"/"QR"` = ?

  • `"XZ"/"PR"`

  • `"XZ"/"PQ"`

  • `"XZ"/"QR"`

  • `"YZ"/"PQ"`

Q.1 (A) | Q 8

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

  • 45°

  • 60°

  • 25°

  • 40°

Q.1 (A) | Q 9

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

  • AAA

  • SAS

  • SAA

  • SSS

Q.1 (A) | Q 10

In fig. BD = 8, BC = 12, B-D-C, then `"A(ΔABC)"/"A(ΔABD)"` = ?

  • 2 : 3

  • 3 : 2

  • 5 : 3

  • 3 : 4

Q.1 (B)

SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board Chapter 1 Similarity Q.1 (B)

Solve [1 Mark]

Q.1 (B) | Q 1

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

Q.1 (B) | Q 2

In fig., line BC || line DE, AB = 2, BD = 3, AC = 4 and CE = x, then find the value of x

Q.1 (B) | Q 3

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°

Q.1 (B) | Q 4

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

Q.1 (B) | Q 5

Areas of two similar triangles are in the ratio 144: 49. Find the ratio of their corresponding sides.

Q.1 (B) | Q 6

ΔPQR ~ ΔSUV. Write pairs of congruent angles

Q.1 (B) | Q 7

ΔABC ~ ΔDEF. Write the ratios of their corresponding sides

Q.1 (B) | Q 8

In fig., TP = 10 cm, PS = 6 cm. `"A(ΔRTP)"/"A(ΔRPS)"` = ?

Q.1 (B) | Q 9

Ratio of corresponding sides of two similar triangles is 4:7, then find the ratio of their areas = ?

Q.1 (B) | Q 10

Write the test of similarity for triangles given in figure.

Q.2 (A)

SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board Chapter 1 Similarity Q.2 (A)

Complete the activity [2 Marks]

Q.2 (A) | Q 1

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     .....[______]

Q.2 (A) | Q 2

Observe the figure and complete the following activity


In fig, ∠B = 75°, ∠D = 75°

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

∠C ≅ ∠C         ...[ ______ ]

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

Q.2 (A) | Q 3

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" = (["______"])/(["______"])`

Q.2 (A) | Q 4

In fig., PM = 10 cm, A(ΔPQS) = 100 sq.cm, A(ΔQRS) = 110 sq.cm, then NR?

ΔPQS and ΔQRS having seg QS common base.

Areas of two triangles whose base is common are in proportion of their corresponding [______]

`("A"("PQS"))/("A"("QRS")) = (["______"])/"NR"`,

`100/110 = (["______"])/"NR"`,

NR = [ ______ ] cm

Q.2 (B)

SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board Chapter 1 Similarity Q.2 (B)

[2 Marks]

Q.2 (B) | Q 1

In fig., AB ⊥ BC and DC ⊥ BC, AB = 6, DC = 4 then `("A"(Δ"ABC"))/("A"(Δ"BCD"))` = ?

Q.2 (B) | Q 2

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


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

Q.2 (B) | Q 3

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

Q.2 (B) | Q 4

From given information, is PQ || BC?

AP = 2, PB = 4, AQ = 3, QC = 6

Q.2 (B) | Q 5

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

Q.2 (B) | Q 6

From adjoining figure, ∠ABC = 90°, ∠DCB = 90°, AB = 6, DC = 8, then `("A"(Δ"ABC"))/("A"(Δ"BCD"))` = ?

Q.3 (A)

SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board Chapter 1 Similarity Q.3 (A)

Complete the following activities [3 Marks]

Q.3 (A) | Q 1

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

Q.3 (A) | Q 2

A line is parallel to one side of triangle which intersects remaining two sides in two distinct points then that line divides sides in same proportion.

Given: In ΔABC line l || side BC and line l intersect side AB in P and side AC in Q.

To prove: `"AP"/"PB" = "AQ"/"QC"`

Construction: Draw CP and BQ

Proof: ΔAPQ and ΔPQB have equal height.

`("A"(Δ"APQ"))/("A"(Δ"PQB")) = (["______"])/"PB"`   .....(i)[areas in proportion of base]

`("A"(Δ"APQ"))/("A"(Δ"PQC")) = (["______"])/"QC"`  .......(ii)[areas in proportion of base]

ΔPQC and ΔPQB have [______] is common base.

Seg PQ || Seg BC, hence height of ΔAPQ and ΔPQB.

A(ΔPQC) = A(Δ______)    ......(iii)

`("A"(Δ"APQ"))/("A"(Δ"PQB")) = ("A"(Δ "______"))/("A"(Δ "______"))`   ......[(i), (ii), and (iii)]

`"AP"/"PB" = "AQ"/"QC"`   .......[(i) and (ii)]

Q.3 (A) | Q 3

From fig., seg PQ || side BC, AP = x + 3, PB = x – 3, AQ = x + 5, QC = x – 2, then complete the activity to find the value of x.

In ΔPQB, PQ || side BC

`"AP"/"PB" = "AQ"/(["______"])`    ...[______]

`(x + 3)/(x - 3) = (x + 5)/(["______"])`

(x + 3) [______] = (x + 5)(x – 3)

x2 + x – [______] = x2 + 2x – 15

x = [______]

Q.3 (B)

SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board Chapter 1 Similarity Q.3 (B)

[3 Marks]

Q.3 (B) | Q 1

There are two poles having heights 8 m and 4 m on plane ground as shown in fig. Because of sunlight shadows of smaller pole is 6m long, then find the length of shadow of longer pole.

Q.3 (B) | Q 2

In ΔABC, B − D − C and BD = 7, BC = 20, then find the following ratio.

(i) `"A(ΔABD)"/"A(ΔADC)"`

(ii) `"A(ΔABD)"/"A(ΔABC)"`

(iii) `"A(ΔADC)"/"A(ΔABC)"`

Q.3 (B) | Q 3

In given fig., quadrilateral PQRS, side PQ || side SR, AR = 5 AP, then prove that, SR = 5PQ

Q.3 (B) | Q 4

In triangle ABC point D is on side BC (B−D−C) such that ∠BAC = ∠ADC then prove that CA2 = CB × CD

Q.3 (B) | Q 5

In Quadrilateral ABCD, side AD || BC, diagonal AC and BD intersect in point P, then prove that `"AP"/"PD" = "PC"/"BP"`

Q.4

SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board Chapter 1 Similarity Q.4

[4 Marks]

Q.4 | Q 1

Side of equilateral triangle PQR is 8 cm then find the area of triangle whose side is half of the side of triangle PQR.

Q.4 | Q 2

Areas of two similar triangles are equal then prove that triangles are congruent

Q.4 | Q 3

Two triangles are similar. Smaller triangle’s sides are 4 cm, 5 cm, 6 cm. Perimeter of larger triangle is 90 cm then find the sides of larger triangle.

Q.5

SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board Chapter 1 Similarity Q.5

[3 Marks]

Q.5 | Q 1

In fig., PS = 2, SQ = 6, QR = 5, PT = x and TR = y. Then find the pair of value of x and y such that ST || side QR.

Q.5 | Q 2

An architecture have model of building. Length of building is 1 m then length of model is 0.75 cm. Then find length and height of model building whose actual length is 22.5 m and height is 10 m

Solutions for Chapter 1: Similarity

Q.1 (A)Q.1 (B)Q.2 (A)Q.2 (B)Q.3 (A)Q.3 (B)Q.4Q.5
SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board chapter 1 - Similarity - Shaalaa.com

SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board chapter 1 - Similarity

Shaalaa.com has the Maharashtra State Board Mathematics 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board Maharashtra State Board solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. SCERT Maharashtra Question Bank solutions for Mathematics 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board Maharashtra State Board 1 (Similarity) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.

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Concepts covered in 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board chapter 1 Similarity are Properties of Ratios of Areas of Two Triangles, Similar Triangles, Areas of Similar Triangles, Basic Proportionality Theorem (Thales Theorem), Property of an Angle Bisector of a Triangle, Property of Three Parallel Lines and Their Transversals, Converse of Basic Proportionality Theorem, Similarity of Triangles, Criteria for Similarity of Triangles.

Using SCERT Maharashtra Question Bank 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board solutions Similarity exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in SCERT Maharashtra Question Bank Solutions are essential questions that can be asked in the final exam. Maximum Maharashtra State Board 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board students prefer SCERT Maharashtra Question Bank Textbook Solutions to score more in exams.

Get the free view of Chapter 1, Similarity 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board additional questions for Mathematics 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board Maharashtra State Board, and you can use Shaalaa.com to keep it handy for your exam preparation.

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