By Team Aakash Byju's | 8th November 2022
In the Given Figure if DE∥BC, AD = 3 cm, BD = 4 cm & BC = 5 cm. Find (i) AE : EC (ii) the measure of DE.
With the reference to the given image, the correct answers are (i) AE: EC = 3:4 and (ii) DE = 2 cm.
1
7
In the image, it is given that DE is parallel to BC and DE intersects the other two sides AB and AC at two distinct points.
According to Thales Theorem, if a line parallel to any one side of the triangle intersects the other 2 sides at distinct points, then
In a △ABC, if DE ∥ BC, then
AE
EC
AD
DB
we can write
AE
EC
3
4
or
AE: EC = 3:4
Since,
AD
BD
AD
BD
AE
EC
3
4
and
Further, from the image given in the question, it can be noticed that ∠A = ∠A, ∠D = ∠B and ∠E = ∠C
Thus, we can say △ADE and △ABC are similar by Angle-Angle similarity. △ADE ∼ △ABC
We know that in similar triangles, all three sides of one triangle are in proportion with the corresponding sides of the other triangle.
AE
AC
AD
AB
DE
BC
3
4
AD
AD
BD
DE
BC
3
3
4
DE
5
3
7
DE
5
or
DE
15
7
2
1
7
=
=
=
=
=
=
=
=
+
+
(
(
)
)
cm.