Olympiad – Class IX – Mathematics - Triangles

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Question - 1

Given 'p' is the exterior angle of \(\triangle\) PQR and 'q + r' is the sum of interior angles opposite to 'p' Which of the following is true?

  • A p + r = q
  • B p = q + r
  • C p + q = r
  • D r = q - p

Question - 2

Identify the interior opposite angles of the exterior angle ∠ACD of \(\triangle\)ABC

  • A \(\angle B\),\(\angle C\)
  • B \(\angle A\),\(\angle C\)
  • C \(\angle A\),\(\angle B\)
  • D \(\angle B\),\(\angle D\)

Question - 3

A student is asked to draw a triangle whose angles are 90o,90o and 20o Which of the following is possible with the given measures?

  • A He can draw a right angled triangle
  • B He can draw an equilateral triangle.
  • C He cannot draw any triangle
  • D He can draw an obtuse angled triangle.

Question - 4

In the given figure, find the ratio \(\angle ABC\):\(\angle ACD\)

  • A 1:1
  • B 2:1
  • C 1:2
  • D 3:1

Question - 5

In ΔABC, AD⊥BC and \(\angle B\)=\(\angle C\) By which property is ΔADB =ΔADC?

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

Question - 6

An exterior angle of a triangle is 110o and one of the interior opposite angles is 30o

Find the other two angles of the triangle.

  • A 80o,70o
  • B 70o,40o
  • C 110o,40o
  • D 110o,75o

Question - 7

One of the angles of a triangle is 75o If the difference of the other two angles is 35o what is the measure the largest angle of the triangle?

  • A 80o
  • B 75o
  • C 100o
  • D 100o

Question - 8

In the figure, if AB = CF, EF = BD and ∠AFE = ∠DBC, by which condition is \(\triangle AFE\)congruent to ∠CBD?

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

Question - 9

In the given figure, ΔABD ≌ ΔACD, AB = AC,BD = CD.

By which criterion are the triangles congruent?

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

Question - 10

In the given figure, AD is the bisector of ∠A and AB = AC. By which criterion are ∆ABD and ∆ACD congruent?

(i) S.S.S (ii) S.A.S (iii) A.S.A (iv)R.H.S

  • A (i) only
  • B (ii), (iii) and (iv) only
  • C (i) and (iii)
  • D (ii) and (iv) only
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