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Triangles Test - 22

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Triangles Test - 22
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  • Question 1
    1 / -0
    SAS criterion is true when  In two triangles, a pair of corresponding sides are proportional and the included angles are equal then the two triangles are similar.
    Solution
    If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.
    Therefore, D is the correct answer.
  • Question 2
    1 / -0
    If the corresponding angles are equal then the two figures having same number of sides are said to be
    Solution
    The corresponding angles are of the same measure means the figures are similar. 
    Therefore, D is the correct answer.
  • Question 3
    1 / -0
    Anna went to the market to buy some boxes to store things. She was surprised to find boxes one inside the other. They were ....... boxes.
    Solution
    As the boxes were fitting one inside the other they were similar as they were of same shape, but their size was different.
    Therefore, D is the correct answer.
  • Question 4
    1 / -0
    If the same photograph is printed in different sizes, then we say both the photographs are
    Solution
    Photograph being same it is printed in the same shape but in passport size, card size, and mini size. They are said to be similar.
    Therefore, B is the correct answer.
  • Question 5
    1 / -0
    There were three circular tracks made in a park having the same middle point but their radii was different. These tracks will be called
    Solution
    They are said to be similar as the shape is same but size differs.
    Therefore, B  is the correct answer.
  • Question 6
    1 / -0
    Is it true that a Pythagorean Triple can never be made up of all odd numbers?
    Solution
    The square of an odd number is an odd number and the square of an even number is an even number.
    The sum of two even numbers is an even number and the sum of an odd number and an even number is in odd number.
    It can be made with all even numbers, but not with odd. So, the statement is true.
    Therefore, D is the correct answer.
  • Question 7
    1 / -0
    3 triangles are given A,  B,  C. All triangles are

    Solution
    From the geometry of the triangles, it can be observed that the triangles are similar.
    If we stretch $$A$$ we will get $$B$$ and then $$C$$. So the ratio of their sides become same and we get similar triangles.
    So option $$A$$ is correct.
  • Question 8
    1 / -0
    If $$\Delta {ABC} \sim \Delta PQR, \angle{B} = \angle{Q}$$ is said to be ________ .
    Solution
    $$\Delta {ABC} \sim \Delta PQR, \angle{B} = \angle{Q}$$ is said to be SAS similarity postulate.
    Because, SAS Similarity Postulate states, "If an angle of one triangle is congruent to the corresponding angle of another triangle and the sides that include this angle are proportional, then the two triangles are similar."
  • Question 9
    1 / -0
    Which similarity criterion is used for the given triangles?

    Solution
    In $$\triangle ABC$$ using angle sum property,
    $$\angle A+\angle B+\angle C={ 180 }^{ \circ  }\\ { 50 }^{ \circ  }+{ 70 }^{ \circ  }+\angle C={ 180 }^{ \circ  }\\ \Rightarrow \angle C={ 60 }^{ \circ  }$$
    Similarly in $$\triangle PQR$$,
    $$\angle P+\angle Q+\angle R={ 180 }^{ \circ  }\\ { 50 }^{ \circ  }+\angle Q+{ 60 }^{ \circ  }={ 180 }^{ \circ  }\\ \Rightarrow \angle Q={ 70 }^{ \circ  }$$
    Now in$$\triangle ABC$$ and $$\triangle PQR$$,
    $$\angle A=\angle P$$
    $$\angle B=\angle Q$$
    $$\angle C=\angle R$$
    So, $$\triangle ABC\sim \triangle PQR$$ by $$AAA$$ criteria
  • Question 10
    1 / -0
    Which pair of triangles shows congruency by the SSS postulate?

    Solution
    From the figure A triangles are similar by SSS postulate because  three sides of one triangle are congruent to three sides of another triangle.
    Therefore, the given triangles are similar by SSS similarity postulate.
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