sche the following questions
i. In the adjoining figure,
If AB = 7 AC=9, BD=3.5 &CD=4.5
find whether ray AD is bisector of LA .???
plz send it fast..
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sche the following questions
i. In the adjoining figure,
If AB = 7 AC=9, BD=3.5 &CD=4.5
find whether ray AD is bisector of LA .???
plz send it fast..
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Here, we can see that ∠BAC is bisected by AD where AD touches BC at D. BC=BD+DC where, BC=3cm . We also have the values of adjacent sides AB=6cm and AC=5cm .
These satisfy the requirements of angle bisector theorem. Then, by the theorem, we have:
ABBD=ACDC
⇒DC=AC∗BDAB=5∗36=2.5cm
SOLUTION :
(i) Given : AB = 5 cm, AC = 10cm, BD = 1.5 cm and CD = 3.5 cm
First check proportional ratio between sides.
Now,
AB/AC= 5/10 = 1/2
BD/CD =1.5/3.5 = 3/7
Here, AB/AC ≠ BD/CD
[If a line through one vertex of a triangle divides the opposite sides in the ratio of other two sides, then the line bisects the angle at the vertex.]
Hence, AD is not the bisector of ∠ A.
(ii) GIVEN : AB = 4 cm, AC = 6 cm, BD = 1.6 cm and CD = 2.4 cm.
First check proportional ratio between sides.
So, AB/AC = BD/DC
4/6 = 1.6/2.4
⅔ = 2/3
Here, AB/AC = BD/CD
[If a line through one vertex of a triangle divides the opposite sides in the ratio of other two sides, then the line bisects the angle at the vertex.]
Hence, AD is the bisector of ∠ A.
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