You visited us 1 times! Enjoying our articles? Unlock Full Access!

Equal Intercept Theorem

AB=11.7cm, BD...

Question

$A B = 11.7 c m, B D = 5.2 c m, A C = 4.4 c m$ and $A E = 2.8 c m$

Yes

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Ambiguous

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Data insufficient

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B No
Given: AB = 11.7 cm, BD = 5.2 cm, AC = 4.4 cm and AE = 2.8 cm
$\frac{A D}{B D} = \frac{A B - B D}{B D} = \frac{6.5}{5.2} = \frac{5}{4}$
$\frac{A E}{E C} = \frac{A E}{A C - A E} = \frac{2.8}{1.6} = \frac{7}{4}$
Since, $\frac{A D}{B D} \neq \frac{A E}{E C}$
By converse of equal Intercept theorem, DE is not parallel to BC

Suggest Corrections

Similar questions

Construct a quadrilateral $A B C D$ in which $A B = 4.4 c m,$ $B C = 4 c m,$ $C D = 6.4 c m, D A = 2.8 c m$ and $B D = 6.6 c m .$ [ $3$ MARKS]

∆ A B C

D E ∥ B C

A D = 5.7 cm, D B = 9.5 cm, B D = 4.8 cm and E C = 8 cm .

A B = 11.7 cm, A C = 11.2 cm, B D = 6.5 cm and A E = 4.2 cm .

A B = 10.8 cm, A D = 6.3 cm, A C = 9.6 cm and E C = 4 cm .

A D = 7.2 cm, A E = 6.4 cm, A B = 12 cm and A C = 10 cm .

D and E are points on the sides AB and AC respectively of a $Δ A B C$ . In each of the follwing cases, determine whether DE || BC or not.

(i) AD = 5.7 cm, DB = 9.5 cm, AE = 4.8 cm and EC = 8 cm.

(ii) AB = 11.7 cm, AC = 11.2 cm, BD = 6.5 cm and AE = 4.2 cm.

(iii) AB = 10.8 cm, AD = 6.3 cm, AC = 9.6 cm and EC = 4 cm.

(iv) AD = 7.2 cm, AE = 6.4 cm, AB = 12 cm and AC = 10 cm.

△

A B C, D

E

D E

∥

B C

A B = 12 c m, A D = 8 c m, A E = 12 c m a n d A C = 18 c m

A B = 5.6 c m, A D = 1.4 c m, A C = 7.2 c m a n d A E = 1.8 c m

A B = 10.8 c m, B D = 4.5 c m, A C = 4.8 c m a n d A E = 2.8 c m

A D = 5.7 c m, B D = 9.5 c m, A E = 3.3 c m a n d E C = 5.5 c m .

90^{0}

⊥

Join BYJU'S Learning Program