10th Class Mathematics Triangles Question Bank

done Assertion And Reason (MCQs) - Triangles Total Questions - 17

• question_answer1)

  Directions (Q. Nos. 1-17): In the following questions, a statement of assertion (A) is followed by a statement of reason (R).  Mark the correct choice as:

  Assertion (A): All regular polygons of the same number of sides such as equilateral triangles, squares etc. are similar.

  Reason (R): Two polygons of the same number of sides are said to be similar, if their corresponding angles are equal and lengths of corresponding sides are proportional.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer2)

  Assertion (A): In a \[\Delta ABC,\] if \[\left. DE \right\|BC\] and intersects AB at D and AC at E, then \[\frac{AB}{AD}=\frac{AC}{AE}\].

  Reason (R): If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then these sides are divided in the same ratio.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer3)

  Assertion (A): In a \[\Delta ABC,\] D and E are points on sides AB and AC respectively such that \[\text{BD}=\text{CE}\]. If \[\angle B=\angle C,\] then DE is not parallel to BC.

  Reason (R): If a line divides any two sides of a triangle in the same ratio, then the line must be parallel to the third side.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer4)

  Assertion (A): In \[\Delta ABC,\] D and E are the points on sides AB and AC respectively such that \[\left. DE \right\|BC\] and \[\text{AD}:\text{DB}=\text{5}:\text{4}\].

  Then \[ar(\Delta DFE):ar(\Delta CFB)=81:25\].

  Reason (R): The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer5)

  Assertion (A): In two similar triangles ABC and PQR, if their corresponding altitudes AD and PS are in the ratio \[\text{4}:\text{9},\] then the ratio of the areas of \[\Delta ABC\] and \[\Delta PQR\] is \[\text{16}:\text{81}\]

  Reason (R): The ratio of the areas of two similar triangles is equal to the ratio of their corresponding altitudes.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer6)

  Assertion (A): \[\Delta ABC\tilde{\ }\Delta DEF\] such that \[ar(\Delta ABC)=100c{{m}^{2}}\]and \[ar(\Delta DEF)=144c{{m}^{2}}\]. If \[\text{AB}=\text{24 cm},\]then \[\text{DE}=\text{36 cm}\].

  Reason (R): The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding medians

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer7)

  Assertion (A): If the bisector of an angle of a triangle bisects the opposite side, then the triangle is isosceles.

  Reason (R): The internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer8)

  Assertion (A): ABC is a triangle in which \[\text{AB}=\text{AC}\] and D is a point on AC such that \[B{{C}^{2}}=AC\times CD\]. Then \[\Delta ABC\tilde{\ }\Delta BDC\]by SAS similarity criterion.

  Reason (R): If two angles of one triangle are respectively equal to the two angles of another triangle, then the two triangles are similar. This is known as SAS similarity criterion.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer9)

  Assertion (A): If the sides of a triangle are \[\text{3 cm},\] \[\text{4 cm},\] and \[\text{6 cm},\] long, then the triangle is a right angled triangle.

  Reason (R): In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer10)

  Assertion (A): The sum of the distances of \[\text{A}{{\text{D}}^{\text{2}}}+\text{B}{{\text{D}}^{\text{2}}}+\text{B}{{\text{E}}^{\text{2}}}+\text{C}{{\text{E}}^{\text{2}}}\]is\[\text{28}.\text{36}\].

  Reason (R): In right angled triangle, \[{{(Hypotenuse)}^{2}}={{(Perpendicular)}^{2}}+{{(Base)}^{2}}\].

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer11)

  Assertion (A): In \[\Delta ABC,\] \[\left. DE \right\|BC\] such that \[AD=(7x-4)cm,\] \[AE=(5x-2)cm,\] \[DB=(3x+4)cm\] and \[\text{EC}=\text{3x cm}\] then x equal to 5.

  Reason (R): If a line is drawn parallel to one side of triangle to intersect the other two sides at a distant point, then the other two sides are divided in the same ratio.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer12)

  Assertion (A): \[\Delta ABC\tilde{\ }\Delta DEF\] such that \[ar(\Delta ABC)=36c{{m}^{2}}\]and \[ar(\Delta DEF)=49c{{m}^{2}}\] then, \[\text{AB}:\text{DE}=\text{6}:\text{7}\].

  Reason (R): If \[\Delta ABC\tilde{\ }\Delta DEF,\] then \[\frac{ar(\Delta ABC)}{ar(\Delta DEF)}=\frac{A{{B}^{2}}}{D{{E}^{2}}}=\frac{B{{C}^{2}}}{E{{F}^{2}}}=\frac{A{{C}^{2}}}{D{{F}^{2}}}\]

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer13)

  Assertion (A): \[\Delta ABC\] is an isosceles triangle right angled at C, then \[A{{B}^{2}}=2A{{C}^{2}}\].

  Reason (R): In right \[\Delta ABC,\] right angled at B, \[A{{C}^{2}}=A{{B}^{2}}+B{{C}^{2}}\]

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer14)

  Assertion (A): Two similar triangles are always congruent.

  Reason (R): If the areas of two similar triangles are equal then the triangles are congruent.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer15)

  Assertion (A): ABC is an isosceles, right triangle, right angled at C. Then \[A{{B}^{2}}=3A{{C}^{2}}\]

  Reason (R): In an isosceles triangle ABC if \[\text{AC}=\text{BC}\] and \[A{{B}^{2}}=2A{{C}^{2}},\]then \[\angle C=90{}^\circ \]

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer16)

  Assertion (A): ABC and DEF are two similar triangles such that \[\text{BC}=\text{4cm},\] \[\text{EF}=\text{5cm}\] and area of \[\Delta ABC=64\,c{{m}^{2}},\] then area of \[\Delta DEF=100\,c{{m}^{2}}\].

  Reason (R): The areas of two similar triangles are in the ratio of the squares of the corresponding altitudes.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer17)

  Assertion (A): In the \[\Delta ABC,\] \[\text{AB}=\text{24 cm,}\] \[\text{BC}=\text{1}0\text{ cm}\] and \[\text{AC}=\text{26cm},\]then \[\Delta ABC\]is a right angle triangle.

  Reason (R): If in two triangles, their corresponding angles are equal, then the triangles are similar.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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