Congruent Triangles

Two figures are congruent, if they are of the same shape and of the same size.

Two circles of the same radii are congruent.

Two squares of the same sides are congruent.

If two triangles ABC and PQR are congruent under the correspondence A ? P, B ? Q and C ? R, then symbolically, it is expressed as ? ABC ? ? PQR.

If two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle, then the two triangles are congruent by SAS Congruence Rule.

If two angles and the included side of one triangle are equal to two angles and the included side of the other triangle, then the two triangles are congruent by ASA Congruence Rule.

In a triangle, side opposite to the larger (greater) angle is longer.

If two angles and one side of one triangle are equal to two angles and the corresponding side of the other triangle, then the two triangles are congruent by AAS Congruence Rule.

Angles opposite to equal sides of a triangle are equal.

Sides opposite to equal angles of a triangle are equal.

Each angle of an equilateral triangle is of 60°.

If three sides of one triangle are equal to three sides of the other triangle, then the two triangles are congruent by SSS Congruence Rule.

If in two right triangles, hypotenuse and one side of a triangle are equal to the hypotenuse and one side of other triangle, then the two triangles are congruent by RHS Congruence Rule.

In a triangle, angle opposite to the longer side is larger or greater.

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  • Q1

    In the given figure it is given that AB = CF, EF = BD and AFE = DBC . Then the congruence of AFE and CBD is given by

    Marks:1
    Answer:

    SAS congruence criterion

    Explanation:

    We have, AB = CF
    So, AB + BF = BF + CF
    Thus, AF = BC
    It is given that EF = BD and AFE = DBC
    AFE CBD (by SAS rule)

    View Answer
  • Q2

    Two triangles are congruent, if they satisfy the criteria of

    Marks:1
    Answer:

    Angle-Side-Angle(ASA)

    Explanation:

    If two angles and the included side of one triangle are equal to two angles and the included side of the other triangle, then the two triangles are congruent.

    View Answer
  • Q3

    The criterion, which holds for the congruency of two triangles is

    Marks:1
    Answer:

    AAS.

    Explanation:

    In AAS criterion, two triangles are congruent if any two pairs of angles and one pair of corresponding sides are equal.

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  • Q4

    The criterion, which does not hold for the congruency of two triangles is

    Marks:1
    Answer:

    ASS.

    Explanation:

    In ASS criterion, equal angles are not included between the pairs of equal sides.

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  • Q5

    ABC EFG, AB = 15 cm, BC = 20 cm, AC = 25 cm and FG = 3x – 7, then the value of x is

    Marks:1
    Answer:

    9 cm

    Explanation:

    Given ABC EFG, hence by CPCT AB = EF, BC = FG and CA = GE.
    Also, A = E, B = F and C = G.

    Now, we have
    FG = 3x – 7 = 20
    3x = 20 + 7
    3x = 27
    x = 9
    View Answer