Mathematics

Question

In the figure CD is the perpendicular bisector of AB . If the length of AC is 2x and the length of BC is 3x - 5 . The value of x is ? ( see diagram ) please help and explain if possible :)
In the figure CD is the perpendicular bisector of AB . If the length of AC is 2x and the length of BC is 3x - 5 . The value of x is ? ( see diagram ) please hel

2 Answer

  • Answer

    Find out the value of x .

    To proof

    SAS congurence property

    In this property two sides and one angle of the two triangles are equal.

    in the Δ ADC and ΔBDC

    (1) CD = CD (common side of both the triangle)

    (2) ∠CDA = ∠ CDB = 90 °

    ( ∠CDA +∠ CDB = 180 ° (Linear pair)

    as given in the diagram

    ∠CDA  = 90°

    ∠ CDB = 180 ° - 90°

    ∠ CDB = 90°)

    (3) AD = DB (as shown in the diagram)

    Δ ADC ≅ ΔBDC

    by using the SAS congurence property .

    AC = BC

    (Corresponding sides of the congurent triangle)

    As given

    the length of AC is 2x and the length of BC is 3x - 5 .

    2x = 3x - 5

    3x -2x =5

    x = 5

    The value of x is 5 .

    Hence proved


  • Answer with Step-by-step explanation:

    We will prove the SAS congruence property

    (In this property two sides and one angle of the two triangles are equal the, the two triangles are similar)

    consider,  Δ ADC and ΔBDC

    (1) CD = CD (common side of both the triangle)

    (2) ∠CDA = ∠ CDB = 90 °

    ( since, ∠CDA +∠ CDB = 180 ° )

    (3) AD = DB (as shown in the diagram)

    Hence, Δ ADC ≅ ΔBDC

    by using the SAS congurence property .

    AC = BC

    (Corresponding sides of the congruent triangle)

    i.e. 2x = 3x - 5

        3x -2x =5

          x = 5

    Hence, the value of x is 5

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