if ad equals to 8 cm ab equal to 12 cm and ae equal to 12 cm find CE
Answers
Given:
✰ AD = 8 cm
✰ AB = 12 cm
✰ AE = 12 cm
To find:
✠ CE.
Solution:
Construction:
In ∆ABC,
D is the point on side AB
E is the point on side AC
DE || BC
As we know that D is the point on side AB, so if we substract AD from AB, we will easily get side BD, so
➛ BD = AB - AD
➛ BD = 12 - 8
➛ BD = 4 cm
The basic proportionality theorem states that the line drawn parallel to one side of a triangle, intersecting the other two sides of a triangle, divides the other two sides in same proportion or in same ratio.
By Thales theorem i.e, by basic proportionality theorem, we have:
➤ AD/DB = AE/CE
➤ 8/4 = 12/CE
➤ 2 = 12/CE
➤ 2CE = 12
➤ CE = 12/2
➤ CE = 6 cm
Therefore, the value of side CE = 6 cm
_______________________________
Answer:
BD = DB
BD = AB - AD
= 12 - 8
= 4cm
Therefore DB = 4cm
AD / DB = AE / CE
8 / 4 = 12 / CE
2 = 12 / CE
2CE = 12
CE = 12 / 2
CE = 6cm