Question

In the given figure, DE || BC and BD=DC.

I) Prove that DE bisects angle ADE
II) If AD=4.5 cm, AE=3.9 cm and DC=7.5 cm, find CE.
III) Find the ratio AD:DB.

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Answer 1

Answer:

1) DE bisects ∠ ADE

2) CE = 6.5 cm

3) AD : DB = 12 : 7.5

Explanation:

(1) We know that DE || BC:

∠ EDC = ∠DCB ( alternate interior angles)

∠ADE = ∠DBC ( corresponding angles.

Also ∠DBC =∠DCB ( Isosceles triangle - BD = DC)

So, we get  ∠ EDC = ∠ADE.

Hence,  DE bisects ∠ ADE.

(2)We know that:

Δ ADE ∼ Δ ABC (AAA rule)

AD / AB = AE / AC

4.5 / 12 = 3.9 / (3.9 +  CE)

Solving it, we get:

CE = 6.5 cm.

(3) AD : DB = AD : DC = 12 : 7.5.

Therefore, DE bisects ∠ ADE, CE = 6.5 cm and AD : DB = 12 : 7.5.

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