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
Question
2 Answer

1. User Answers JackelineCasarez
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

2. User Answers erato
Answer with Stepbystep 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