In a -ABC- if D is a point on BC such that BD-DC-AB-AC- then which of the following is always correct-

Given:BD/DC = AB/BC Construction: Extend BA to P such that AP = AC and join PC. Now, given that .BD/DC = AB/AC BD/DC = AB/AP By converse of Basic Proportionali ...

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

Byju's Answer

Standard X

Mathematics

Converse of Basic Proportionality Theorem

In a ΔABC, if...

Question

In a $Δ A B C$ , if D is a point on BC such that $\frac{B D}{D C} = \frac{A B}{A C}$ , then which of the following is always correct?

B D = D C

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

∠ A D B = ∠ A D C

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

∠ B A D = ∠ C A D

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

A D = D C

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

Open in App

Solution

The correct option is C $∠ B A D = ∠ C A D$
Given: $\frac{B D}{D C} = \frac{A B}{B C}$
Construction: Extend BA to P such that AP = AC and join PC.

Now, given that . $\frac{B D}{D C} = \frac{A B}{A C}$
$\frac{B D}{D C} = \frac{A B}{A P}$
By converse of Basic Proportionality Theorem, $A D | | P C$
$∠ B A D = ∠ A P C$ (Corresponding angles) ..…(i)
$∠ C A D = ∠ A C P$ (Alternate interior angles) …..(ii)
Also, by construction, $A C = A P$ .
$\Rightarrow ∠ A C P = ∠ A P C$ (Angles opposite to equal sides are equal) ..…(iii)
Thus, from (i), (ii) and (iii),
$∠ B A D = ∠ C A D$
Hence, the correct answer is option (3).

Suggest Corrections

Similar questions

Q. In a

Δ A B C

, if point D is on the BC such that

\frac{A B}{A C} = \frac{B D}{D C}

and

∠ B = 70^{\circ}, ∠ C = 50^{\circ}

.
Find

∠ B A D

Q. In

Δ A B C

, D is a point on BC such that AB = AD = BD = DC. then

∠ A D C : ∠ C = 4 : 1

State whether the above statement is true or false.

In $Δ$ ABC, D is a point on BC such that AB= AD = BD =DC. Show that : $∠$ ADC : $∠$ C = 4: 1.

Q. In

Δ A B C

, AB = AC and D is a point on side AC such that AD = BD = BC. Show that :

∠ A D B = 108^{\circ}

Q. In

Δ A B C, ∠ A B C = 90^{\circ} A B = 3 c m

and

B C = 4 c m

. If

B D ⊥ A C

where

D

is a point on

A C

, then find

B D

Join BYJU'S Learning Program

In a ΔABC, if D is a point on BC such that BDDC=ABAC, then which of the following is always correct?

In a $Δ A B C$ , if D is a point on BC such that $\frac{B D}{D C} = \frac{A B}{A C}$ , then which of the following is always correct?