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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 class=

Verified 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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