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Congruence of Triangles Test - 7

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Congruence of Triangles Test - 7
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Weekly Quiz Competition
  • Question 1
    1 / -0
    Which of the following statements is/are CORRECT?

    1. Two triangles which are congruent have same perimeter.
    2. If two angles and a side of two triangles are equal, then those triangles are congruent.
    3. If each side of a triangle is equal to each side of another triangle, then the triangles are called congruent.
    4. All of these
    Solution
    Two triangles which are congruent have same perimeter. In congruent triangles, all sides are same, hence they will have same perimeter.
    If two angles and a side of two triangles are equal, then those triangles are congruent.



    If each side of a triangle is equal to each side of another triangle, then the triangles are called congruent.



    Hence, all of these statements are correct.
  • Question 2
    1 / -0
    In a triangle PQR, PQ = PR. If PS is a bisector drawn on QR, then the property by which △PQS is congruent to △PRQ is
    Solution

    In triangles PQS and PRS,
    PQ = PR (given)
    QS = SR (given)
    PS = PS (common)
    Hence, △PQS is congruent to △PRS by SSS.
  • Question 3
    1 / -0
    On the basis of the given figure, which of the following options is true?


    Solution
    In the given figure:
    Consider △RQP and △RTS
    PR = RS (given)
    QR = RT (given)
    QPR = RST
    So, by SAS property:
    As it can be seen, △RQP is congruent to △RTS.
    Therefore Q = T (cpct)
  • Question 4
    1 / -0
    By which of the following criteria are the given triangles RST and UVT congruent?


    Solution


    In triangles RST and UVT,
    ∠RTS =∠UTV (Vertically opposite angles)
    ∠S = ∠V (given)
    RT = TU
    Therefore, RST is congruent to UVT by AAS.
  • Question 5
    1 / -0
    In the given figure, if A = C, AE is perpendicular to ED and DC is perpendicular to ED, then AD is equal to


    Solution

    As it can be seen, AED =CDE = 90o
    A = C
    ED = DE (common)
    Therefore, △AED ≌ △CDE
    Hence, AD = CE
  • Question 6
    1 / -0
    If the following triangles are proved congruent by using RHS rule, then


    Solution


    As it can be seen,
    C = F = 90o
    AB = DE
    AC = DF
    △ABC ≅ △DEF (By RHS)
  • Question 7
    1 / -0
    By which of the following criteria can the given triangles be proved congruent?


    Solution

    As it can be seen,
    B = E = 90o
    AB = ED
    BC = EF
    △ABC ≅ △DEF (By RHS or SAS)
  • Question 8
    1 / -0
    If ΔABC ≅ ΔDFE, A = 110° and E = 50°, find the measure of F.

    Solution
    ΔABC ≅ ΔDFE
    A = D = 110° and E = 50°
    In △DFE,
    D + E+ F = 180°
    110° + 50° + F = 180°
    F = 20°
  • Question 9
    1 / -0
    If △EFG ≅ △XYZ, then F and EG are respectively equal to
    Solution

  • Question 10
    1 / -0
    Consider the given figure:

    If QR = RT and ST is parallel to QP, then which of the following options is true?
    Solution

    In and ,
    Q = T (Alternate angles)
    P = S (Alternate angles)
    QR = RT
    Therefore, △ RQP ≅ △RTS (By AAS)
  • Question 11
    1 / -0
    Look at the following figure and tell which of the following relations is incorrect.


    Solution


    From the given figure it is clear that △ABE ≅ △CDE.

    Therefore, AE = EC, and not DE
  • Question 12
    1 / -0
    In the given figure, △MON ≅ △ROP by the _______________ congruency rule.


    Solution


    M = R (given)
    MON = ROP = 70o
    MO = RO
    △MON ≅ △ROP (By ASA)
  • Question 13
    1 / -0
    Which congruence criterion can be used to state that △ABC ≅ △DEF?


    Solution

    As it can be seen, there are two angles and one side, so AAS criterion can be used to prove them congruent.
  • Question 14
    1 / -0
    Directions: Study the following figure and information carefully and answer the question that follows.

    In the given figure, AB = AE, and C and D are the midpoints of AB and CE, respectively.



    △ADB is congruent to
    Solution
    In △ADB and △ACE,
    AB = AE (given)
    AD = AC (given)
    A = A (common)
    △ADB ≅ △ACE (By SAS)
  • Question 15
    1 / -0
    Directions: Study the following figure and information carefully and answer the question that follows.

    In the given figure, AB = AE, and C and D are the midpoints of AB and CE, respectively.



    AEC is equal to
    Solution
    In △ADB and △ACE,
    AB = AE (given)
    AD = AC (given)
    A = A (common)
    △ADB ≅ △ACE (By SAS)
    Therefore, AEC = ABD

  • Question 16
    1 / -0
    Pick the odd one out.
    Solution
    In all the options except option (1), the triangles can be proved congruent by using AAS and ASA criteria.
  • Question 17
    1 / -0
    If ABC and EFG are two triangles, and BA = EG, BC = EF and ∠B =∠E, then which of the following options is true?
    Solution


    △ABC ≅ △GEF (By SAS)
  • Question 18
    1 / -0
    Which of the following is correct for the given diagram?


    Solution
    In △ABC and △CDA,
    AB = CD
    BC = DA
    CA = AC
    △ABC ≅ △CDA (By SSS)
  • Question 19
    1 / -0
    If in triangles MNO and PQR, MN = PQ, NO = QR and OM = RP, then which of the following statements is correct?
    Solution
    MN = PQ
    NO = QR
    OM = RP
    △MNO ≅ △PQR (By SSS)

  • Question 20
    1 / -0
    In the given figure, if DA = BC and CD = AB, then which of the following options is true?


    Solution
    DA= BA
    CD = AB
    AC = CA
    △ABC ≅ △CDA (By SSS)
    Hence, DCA = BAC
  • Question 21
    1 / -0
    The shape of the roof of a building is as given below. If BED = BEF, then what other condition can make △BED ≌ △BEF?


    Solution
    In △BED and △BEF,
    BE = BE (Common side)
    BED = BEF (90o)
    So, if DE = EF, then both the triangles are congruent by SAS criterion.
  • Question 22
    1 / -0
    A reflection of a triangle ABC can be seen in plane mirror as given below. Which of the following options is/are true?


    Solution
    As both the triangle and its image are congruent to each other, because the corresponding sides will be equal, the angles and sides must be the same.
  • Question 23
    1 / -0
    Consider the given figure and choose the correct option.


    Solution
    BA = AM = MC = CN = ND = DE
    AM + MC = CN + ND
    AC = CD
    And AB = DE
    BC = CE
    So, by SSS criterion, triangles ABC and DEC are congruent.
  • Question 24
    1 / -0
    Three students A, B and C write 3 statements.

    A writes ''Congruent triangles are always equal in size.''
    B writes ''All similar triangles are congruent.''
    C writes ''If two triangles are equal, then their corresponding sides are equal.''

    Who write(s) an incorrect statement?
    Solution
    If two triangles are similar, then it is not always true that they are congruent.
    Similarity means that they are equal in shape but not always in size.
  • Question 25
    1 / -0
    A truck has a container attached to its backside having length 8 m and breadth 9 m. Find the length(approximate) of DC knowing that all the corners are 90ο and the opposite sides are parallel.

    Solution


    According to the diagram and given conditions, ABCD is a rectangular shape.
    And in a rectangle, the triangles are congruent to each other.
    So, triangles ACB and DCB are congruent to each other.
    This results in AC = DB.

    Now applying Pythagoras theorem,
    92 + 82 = H2
    81 + 64 = H2
    145 = H2
    H = 12 m (approximately)
  • Question 26
    1 / -0
    Match the following:
    Column-I Column-II

    1.
    		(a) AAS postulate

    2.
    		(b) SAS postulate

    3.
    		(c) ASA postulate

    4.
    		(d) SSS postulate
    Solution
    1. If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
    [SAS postulate]

    2. If two angles and a non included side of one triangle are congruent to two angles and the corresponding non included side of another triangle, then the triangles are congruent.
    [AAS postulate]

    3. If three sides of one triangle are congruent to three sides of another, then the two triangles are congruent.
    [SSS postulate]

    4. If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
    [ASA postulate]
  • Question 27
    1 / -0
    Which of the following statements is correct?

    Statement I: If two pairs of sides of two triangles are equal in length, and the included angles are equal in measurement, then the triangles are congruent.
    Statement II: If two pairs of angles of two triangles are equal in measurement, and the included sides are equal in length, then the triangles are congruent.
    Solution
    Both the statements are true
    If two pairs of sides of two triangles are equal in length, and the included angles are equal in measurement, then the triangles are congruent. It is called SAS criterion.
    If two pairs of angles of two triangles are equal in measurement, and the included sides are equal in length, then the triangles are congruent. It is called ASA criterion.
  • Question 28
    1 / -0
    Which of the following statements is incorrect?
    Solution
    A scalene triangle can be acute or obtuse.
    Thus, scalene triangles are not always acute.


  • Question 29
    1 / -0
    Which of the following statements is TRUE?
    Solution
    If two isosceles triangles have one angle in common, then these are congruent triangles.
    (By SAS rule)
  • Question 30
    1 / -0
    State 'T' for true and 'F' for false.

    1. Two line segments are said to be congruent plane figures if and only if their lengths are equal.
    2. Two triangles which look similar are also congruent.
    3. Two rectangles are said to be congruent plane figures if and only if one of them can be made to superimpose on the other so as to cover it exactly.
    4. In a square, only two angles are congruent to each other.
    5. Two circles are congruent if and only if they have equal radius.
    Solution
    1. Two line segments are equal and congruent only when they are equal in lengths.
    2. Congruent figures are similar, but not vice versa.
    3. If two plane figures can superimpose each other completely, then they are called congruent.
    4. In a square, each angle is 90°; so all the four angles are congruent to each other.
    5. Two circles with equal radius are congruent.
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