Olympiad – Class VII – Mathematics - Congruence of Triangles

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Question - 1

In \(\triangle\)ABC, AB = AC and AD is perpendicular to BC. State the property by which \(\triangle\)ADB \(\cong \) \(\triangle\)ADC.

  • A S.A.S. property
  • B S.S.S.property
  • C R.H.S.property
  • D A.S.A. property

Question - 2

Two students drew a line segment each. What is the condition for them to be congruent?

  • A They should be drawn with a scale.
  • B They should be drawn on the same sheet of paper.
  • C They should have different lengths
  • D They should have the same length.

Question - 3

In the given figure, if AD = BCand ADIIBC, which of the following is true?

  • A AB = AD
  • B AB = DC
  • C BC=CD
  • D AC=AD

Question - 4

In\(\triangle\) PQR and \(\triangle\) XYZ,\(\angle\) P = 50°, XY = PQ, and XZ = PR.By which property are\(\triangle\) XYZ and \(\triangle\)PQR congruent?

  • A S.S.S,property
  • B S.A.S.property
  • C A.S.A property
  • D R.H.S.property

Question - 5

A: Two triangles are said to be congruent if two sides and an angle of one triangle are respectively equal to the two sides and an angle of the other.
R : Two triangles are congruent if two sides and the included angle of one are equal to the corresponding two sides and included angle of the other.
Given A & R, which of the following statements is correct?

  • A A is false and R is the correct explanation of A.
  • B A is true and R is the correct explanation of A.
  • C A is true and R is false.
  • D A is false and R is true.

Question - 6

Two triangles, \(\triangle\) PQR and \(\triangle\)DEF are of the same size and shape. What can we conclude about them?

  • A \(\triangle\)PQR is smaller than \(\triangle\)DEF
  • B \(\triangle\)PQR is larger than \(\triangle\)DEF
  • C \(\triangle\)PQR is congruent to \(\triangle\)DEF
  • D \(\triangle\)PQR is not congruent to \(\triangle\)OEF

Question - 7

Which of the following examines the congruence of plane figures?

  • A Trial and error method
  • B Superposition method
  • C Substitution method
  • D Transposition method

Question - 8

Which of the following is a pair of congruent figures?

  • A A regular pentagon and a regular hexagon.
  • B A rhombus and a square
  • C Two equilateral triangles of the same length of their sides.
  • D A quadrilateral and a rectangle.

Question - 9

In \(\triangle\)ABC and \(\triangle\)PQR,AB = x cm, BC= ycm and CA = z cm. What are the measures of sides PQ, QR and RP of\(\triangle\)PQR if \(\triangle\)ABC \(\cong \)\(\triangle\)ABC \(\cong \)\(\triangle\)PQR?

  • A PQ QR RP x cm y cm z cm
  • B PQ QR RP y cm x cm z cm
  • C PQ QR RP x cm z cm y cm
  • D PQ QR RP z cm x cm y cm

Question - 10

In the given figure, AD = CD and AB=CB.

What are the three pairs of equal parts?

  • A \(\angle\)ADB =\(\angle\)CDB, \(\angle\)ABD = \(\angle\)CBD; BD= BD
  • B AD = AB, DC = CB,BD = BD
  • C AB = CD,AD = BC,BD = BD
  • D \(\angle\)ADB =\(\angle\)CDB, \(\angle\)ABD = \(\angle\)CBD:\(\angle\)DAB = \(\angle\)DBC