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Triangles Test - 2

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Triangles Test - 2
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Weekly Quiz Competition
  • Question 1
    1 / -0
    XYZ represents a scalene triangle only if
    Solution
    A triangle which has all the three angles different is known as scalene triangle.
    So, XYZ represents a scalene triangle only if X Y Z, i.e. all the angles are unequal.
  • Question 2
    1 / -0
    If the vertical angle of an isosceles triangle is 70°, each base angle is of measure _____.
    Solution
    Let one of the base angles be x°.
    70° + x° + x° = 180° (Angle sum property of the triangle)
    70° + 2x° = 180°
    2x° = 180° - 70°
    2x° = 110°
    x° = 55°
  • Question 3
    1 / -0
    If PQR XYZ indicates the one–to–one correspondence between two triangles, which of the following statements is not true?
    Solution
    XZY is the corresponding angle of RPQ.


    XZY is the corresponding angle of PRQ, not of RPQ.
  • Question 4
    1 / -0
    Which of the following isosceles triangles is not an acute triangle?
    Solution
    In XYZ, X + Y + Z = 180° (Angle sum property)
    40° + 40° + X = 180°
    80° + X = 180°
    X = 100°
    Since one of the angles is greater than 90° in XYZ, so XYZ is not acute.
  • Question 5
    1 / -0
    What will be the measure of the three angles of a triangle with each side 5 cm?
    Solution
    All the sides of the triangle is 5 cm i.e. all the sides are equal in length. So, it is an equilateral triangle. Also, in equilateral triangle, all the angles are of 60°.
  • Question 6
    1 / -0
    Which of the following statements is always true about an isosceles triangle?
    Solution
    Statement 1: Sum of any two angles will be less than the third angle.This is a false statement.Ex: 50o, 50o ,80o

    Statement 2: Sum of the equal angles will be greater than or equal to 90°.This is also a false statement. Ex: 40o, 40o ,100o

    Statement 3: The vertical angle will be greater than each of the base angles.This is also a false statement. Ex: 70o, 70o , 40o

    Statement 4: The statement that the measure of the vertical angle can be anything between 0° and 180° is always true about an isosceles triangle.
  • Question 7
    1 / -0
    Which of the following triplets represents the angles of a scalene triangle?
    Solution
    In a scalene triangle, all the sides and angles are unequal.

    Option 1: Two of the angles of xo, xo, 3xo are same which means that the triangle formed by these angles is isosceles triangle and not scalene.
    Option 2 : All the angles are different which means that the triangle formed by these angles is scalene triangle.
    Option 3: All the angles (2xo, 2xo, 2xo) are same which means that the triangle formed by these angles is equilateral triangle and not scalene.

    Option 4: Here, the angles (x + 10)o, (100 - 2x)o and (x - 40)o are looking different but if we take (x - 40) = (100 - 2x), then x = (140/3)o, for which two of the angles become equal and the triangle will become isosceles triangle.

    Therefore, Option 2 is correct.
  • Question 8
    1 / -0
    Which of the following statements is always true for an obtuse triangle?
    Solution
    According to the angle sum property of a triangle, the sum of all the angles of a triangle is 180°. Therefore, if the measure of one angle is greater than 90°, then the other two angles will be acute with sum less than 90°.
  • Question 9
    1 / -0
    If two quadrilaterals ABCD and PQRS are similar, which of the following relationships is not true?
    Solution
    As in case of similar quadrilaterals ABCD and PQRS, all the sides of quadrilateral ABCD should come in the numerator and all the sides of quadrilateral PQRS should come in the denominator, so the relationship is not true.
  • Question 10
    1 / -0
    Which of the following statements is never true about an isosceles triangle?
    Solution
    Sum of two angles is equal to the third angle except for a right-angled triangle.
    The above statement can never be true about an isosceles triangle because only two angles in an isosceles triangle are equal and their sum can be greater or less than the measure of third angle.
  • Question 11
    1 / -0
    Which of the following triangles can never be an obtuse triangle?
    Solution
    A right-angled triangle has one angle equal to 90°. So the sum of other two angles is also 90° or each of the other two angles is less than 90°. Hence, a right-angled triangle can never be an obtuse triangle.
  • Question 12
    1 / -0
    Which of the following statements is always true about two equiangular triangles?
    Solution
    The three angles of the first triangle are equal to their corresponding angles in the second triangle.
    When two triangles are equiangular then the three angles of the first triangle are equal to the corresponding angles of the second triangle.
  • Question 13
    1 / -0
    Which of the following triangles can never be a scalene triangle?
    Solution
    A scalene triangle is the one in which all the sides are of unequal lengths, where as in an equilateral triangle all the sides are of equal length. So, an equilateral triangle can never be a scalene triangle.
  • Question 14
    1 / -0
    In ABC and PQR, AC = PQ, AB = PR and BC = RQ. Which of the following options represents their one-to-one correspondence?
    Solution




    Hence, PQR ACB.
  • Question 15
    1 / -0
    If ABC MLN, which of the following statements is true?
    Solution
    If ABC MLN, then AB = ML because in case of congruent triangles, corresponding sides are equal.
  • Question 16
    1 / -0
    Which of following conditions may be true for an isosceles triangle with sides a, b and c?
    Solution
    In case of an isosceles triangle, two sides are equal. But even if all the three sides are equal as in an equilateral triangle, then also it is an isosceles triangle.
  • Question 17
    1 / -0
    Which of the following statements is correct?
    Solution
    Two circles cannot be congruent if they have different radii. Two squares can only be congruent if their sides are equal. Two rectangles are equiangular but their corresponding sides may or may not be proportional. So, none of these is a correct statement.
  • Question 18
    1 / -0
    Which of following statements is true about obtuse triangles?
    Solution
    According to the angle sum property of a triangle, if one angle of a triangle is greater than 90°, then the other two angles must be acute angles. Therefore, an obtuse triangle can have only one obtuse angle.
  • Question 19
    1 / -0
    If , and are the angles of an isosceles triangle, which of following statements may be true for an isosceles triangle?
    Solution
    If , and are the angles of an isosceles triangle, then the statement a = may be true for an isosceles triangle because two angles of an isosceles triangle are equal.
  • Question 20
    1 / -0
    Which of the following triangles is always acute?
    Solution
    An acute angle is less than 90°. In an equilateral triangle all the angles are of 60°, therefore an equilateral triangle is always acute.
  • Question 21
    1 / -0
    Which of following triangles is obtuse?
    Solution
    An obtuse triangle has one of the angles obtuse i.e. > 90°. As the third angle of triangle VUW is of measure 130° (Sum of the angles of triangle is 180°), So triangle VUW is an obtuse triangle.
  • Question 22
    1 / -0
    ABC is a scalene triangle. Which of the following relationships is always true regarding ABC?
    Solution
    In a scalene triangle, all the three sides are unequal. So if ABC is scalene, then AB BC CA.
  • Question 23
    1 / -0
    ABC and PQR are two equilateral triangles. Which of the following statements is not true?
    Solution
    If two triangles are equilateral, then they are equiangular, but the sides of one triangle may or may not be equal to the sides of the other triangle.
  • Question 24
    1 / -0
    Which of following triangles can never be acute?
    Solution
    In an acute triangle, the measure of all the angles is less than 90°, whereas in case of a right-angle triangle, one angle is of 90°, so it can never be an acute triangle.
  • Question 25
    1 / -0
    In triangle PQR and triangle LMN, P = L and R = M. Which of the following options represents their one-to-one correspondence?
    Solution
    In PQR and LMN,
    P = L,
    R = M
    So, Q = N (By angle sum property)
    Also, both the triangles are similar.
    Therefore, LMN PRQ represents their one-to-one correspondence.
  • Question 26
    1 / -0
    If ACB ~PQS, which of the following relationships is true?
    Solution
    If ACB ~ PQS, then [because if the two triangles are similar, then their corresponding sides are proportional].
  • Question 27
    1 / -0
    ABC is a right triangle, right-angled at B. BD is perpendicular to side AC. Which of the following statements is correct?
    Solution


    ABC ~ ADB (similar triangles by AA property)
    (similar parts of similar triangles)
    AB2 = AD.AC
  • Question 28
    1 / -0
    If ABC ~ PQR, ar(ABC) = 16 cm2 and ar(PQR) = 16 cm2, which of the following statements is definitely true?
    Solution
    ABC ~ PQR

    =

    =

    1 =

    AB = PQ, BC = QR, AC = PR

    Hence, ABC PQR (By SSS similarity criterion)
  • Question 29
    1 / -0
    MNO ~ PQR, ar(MNO) = 81 cm2 and ar(PQR) = 100 cm2. If MO = 9 cm, then the length of PR is _____.
    Solution
    MNO ~ PQR


    PR = 10 cm
  • Question 30
    1 / -0
    ABC ~ DEF and = . The ratio of the areas of ABC and DEF is ____.
    Solution
    ABC ~ DEF
    Hence,
    =
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