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Uttarakhand Board Class 10 Polygons — practice questions

Explore 30 free Polygons questions in Uttarakhand Board Class 10 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Polygons questions and exercises with answers

Showing questions 1–30 of 30.

Two figures are said to be similar if they haveRead the answer and worked solution →All circles areRead the answer and worked solution →All squares with different side lengths areRead the answer and worked solution →The criterion that uses two pairs of equal angles to prove triangle similarity is calledRead the answer and worked solution →In two similar triangles, the ratio of corresponding sides is calledRead the answer and worked solution →Pythagoras theorem applies to which triangles?Read the answer and worked solution →In triangle ABC, DE is parallel to BC where D lies on AB and E on AC. If AD = 2 cm, DB = 3 cm and AE = 4 cm, then EC equalsRead the answer and worked solution →Two triangles have areas in the ratio 49 : 64. The ratio of their corresponding sides isRead the answer and worked solution →A vertical pole 6 m tall casts a shadow 4 m long at the same time a tower casts a shadow 28 m long. The height of the tower isRead the answer and worked solution →In a right triangle the legs measure 9 cm and 12 cm. The hypotenuse isRead the answer and worked solution →If two triangles are similar and the ratio of their perimeters is 3 : 5, then the ratio of their areas isRead the answer and worked solution →In triangle ABC, AD bisects angle A and meets BC at D. If AB = 6 cm, AC = 9 cm and BC = 10 cm, then BD equalsRead the answer and worked solution →The hypotenuse of a right triangle is 26 cm and one leg is 24 cm. The other leg isRead the answer and worked solution →The altitude AD of an equilateral triangle ABC of side length a isRead the answer and worked solution →In triangle PQR, S and T are points on PQ and PR respectively. ST is parallel to QR. If PS = 3, SQ = 6 and PT = 4, then PR equalsRead the answer and worked solution →A 5 m long ladder leans against a wall with its foot 3 m from the wall. The height it reaches up the wall isRead the answer and worked solution →The diagonals of a rhombus are 16 cm and 30 cm. The length of each side isRead the answer and worked solution →In two similar triangles the ratio of medians is 3 : 5. The ratio of corresponding sides isRead the answer and worked solution →In triangle ABC right-angled at B, BD is perpendicular to AC. If AB = 5 cm and BC = 12 cm, then BD equalsRead the answer and worked solution →D, E, F are midpoints of sides BC, CA, AB of triangle ABC. The ratio of areas of triangle DEF and triangle ABC isRead the answer and worked solution →In a right triangle with legs a and b, the altitude h drawn to the hypotenuse c satisfiesRead the answer and worked solution →In triangle ABC, points P and Q are on AB and AC such that PQ is parallel to BC. If AP = x, PB = 6, AQ = 4, QC = 9, then x equalsRead the answer and worked solution →In an isosceles triangle ABC with AB = AC = 13 cm and BC = 10 cm, the altitude from A to BC isRead the answer and worked solution →Two similar triangles have areas 81 sq cm and 144 sq cm. The ratio of their corresponding altitudes isRead the answer and worked solution →In triangle ABC, AD is perpendicular to BC. Given AB = 7 cm, AC = 25 cm, BD = 5 cm, the value of CD isRead the answer and worked solution →The sides of a triangle are in the ratio 3 : 4 : 5 and its perimeter is 60 cm. The area of the triangle isRead the answer and worked solution →ABC is an equilateral triangle of side 2a. The length of its altitude isRead the answer and worked solution →In a quadrilateral ABCD where AB is parallel to CD and the diagonals AC and BD intersect at O, the ratio AO : OC equalsRead the answer and worked solution →Triangles ABC and DEF are similar with AB = 4 cm, BC = 5 cm, CA = 6 cm and EF = 7.5 cm. The perimeter of triangle DEF isRead the answer and worked solution →In triangle ABC, AB squared + BC squared = AC squared and AB = BC. The angles of the triangle areRead the answer and worked solution →

Worked practice questions

Two figures are said to be similar if they have

  1. The same shape but not necessarily the same size
  2. The same shape and the same size always
  3. Different shapes but the same area
  4. Equal angles but different ratios of sides
Show answer and solution

Correct answer: A. The same shape but not necessarily the same size

1. Definition: similar figures have the same shape but not necessarily the same size. 2. Congruent figures are similar but the converse is not always true. 3. Hence the correct option says "same shape, not necessarily same size". _Source: syllabus Mathematics, Ch 6 "Triangles", §6.2_

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All circles are

  1. Congruent only if radii are equal
  2. Always similar to each other
  3. Always congruent to each other
  4. Never similar unless radii are equal
Show answer and solution

Correct answer: B. Always similar to each other

1. Any two circles have the same shape (round). 2. They differ only by scale (radius), which is the definition of similarity. 3. So all circles are always similar. _Source: syllabus Mathematics, Ch 6 "Triangles", §6.2_

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All squares with different side lengths are

  1. Congruent
  2. Neither similar nor congruent
  3. Similar
  4. Unable to compare
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Correct answer: C. Similar

1. Squares share angles of 90 degrees and all sides equal. 2. A larger square is a scale-up of a smaller one with the same shape. 3. So all squares are similar. _Source: syllabus Mathematics, Ch 6 "Triangles", §6.2_

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More Mathematics topics

SequencesBinomial TheoremGeometryProbability & StatisticsSequences and SeriesVectors & 3D GeometryProbabilityCorrelation and Regression