In triangle ABC, angle BAD = angle CAD, AB = 6cm, AC = 8cm a) Find BD:DC b) Draw a line of length 10cm and divide in the ratio 3:4
Answers
Answer:
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BD : DC = 3 : 4 if in ΔABC ∠BAD = ∠CAD and AB =6cm , AC = 8cm
Given : triangle ABC
∠BAD = ∠CAD
AB = 6 cm
AC = 8 cm
To Find : BD :DC
Solution:
Triangle Angle Bisector Theorem
"A bisector of an angle of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle."
∠BAD = ∠CAD
=> AD is bisector of ∠BAC
Using triangle angle bisector theorem :
AB/ AC = BD/ DC
=> 6/8 = BD/DC
=> 3/4 = BD/DC
=> BD : DC = 3 : 4
in triangle ABC angle BAD = angle CAD, AB =6cm , AC = 8cm then BD :DC is 3 : 4
Draw a lines segment AB = 10 cm
Draw an acute angle BAX using protractor
Using suitable compass width starting from A make 7 points one by one on ray AX
Join 7th point with B
Draw a line parallel to that line passing through 3rd point and intersecting AB at M
M divides AB in 3 : 4 ratio
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