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

Byju's Answer

Standard X

Mathematics

Criteria for Similarity of Triangles

Construct an ...

Question

Construct an equilateral triangle. $Δ A B C$ . Construct an angle bisector of $∠ A$ .
Let it meet side BC at D. Find measures of AB,AC,BD,DC.
Find the relation between $\frac{A B}{A C}$ and $\frac{B D}{D C}$ .

\frac{A B}{A C}

<

\frac{B D}{D C}

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

\frac{A B}{A C}

>

\frac{B D}{D C}

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

\frac{A B}{A C}

=

\frac{B D}{D C}

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

None

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

Open in App

Solution

The correct option is A $\frac{A B}{A C}$ $=$ $\frac{B D}{D C}$
In equilateral triangle ABC,
AB = AC.

So, $\frac{A B}{A C} = 1$

Since, angle bisector of $∠ A$ also bisects BC.
So, BD = DC

Hence, $\frac{B D}{D C} = 1$

Hence, $\frac{A B}{A C} = \frac{B D}{D C}$
So, option C is correct.

Suggest Corrections

Similar questions

Q. If a ∆ ABC, AD is the bisector of ∠A, meeting side BC at D.

(i) If BD = 2.5 cm, AB = 5 cm and AC = 4.2 cm, find DC.
(ii) If BD = 2 cm, AB = 5 cm and DC = 3 cm, find AC.
(iii) If AB = 3.5 cm, AC = 4.2 cm and DC = 2.8 cm, find BD.
(iv) If AB = 10 cm, AC = 14 cm and BC = 6 cm, find BD and DC.
(v) If AC = 4.2 cm, DC = 6 cm and BC = 10 cm. find AB.
(vi) If AB = 5.6 cm, AC = 6 cm and DC = 3 cm, find BC.
(vii) If AD = 5.6 cm, BC = 6 cm and BD = 3.2 cm, find AC.
(viii) If AB = 10 cm, AC = 6 cm and BC = 12 cm, find BD and DC.

Q. In a

△

ABC, AD is the bisector of

∠

A, meeting side BC at D.

(i) If BD = 2.5 cm, AB = 5 cm and AC = 4.2 cm, find DC.

(ii) If BD = 2 cm, AB = 5 cm and DC = 3 cm, find AC.

(iii) If Ab = 3.5 cm, AC = 4.2 cm and DC = 2.8 cm, find BD.

(iv) If AB = 10 cm, AC = 14 cm and BC = 6 cm, find BD and DC.

(v) If AC = 4.2 cm, DC = 6 cm and BC = 10 cm, find AB.

(vi) If AB = 5.6 cm, AC = 6 cmand DC = 3 cm, find BC

(vii) If AD = 5.6 cm, BC = 6 cm and BD = 3.2 cm, find AC

(viii) If AB = 10 cm, AC = 6 cm and BC = 12 cm, find BD and DC.

In a $Δ A B C$ , AD is the bisector of $∠ A$ .

(i) If AB = 6.4 cm, AC = 8 cm and BD = 5.6 cm, find DC.

(ii) If AB = 10 cm, AC = 14 cm and BC = 6 cm, find BD and DC.

(iii) If AB = 5.6 cm, BD = 3.2 cm and BC = 6 cm, find AC.

(iv) If AB = 5.6 cm, AC = 4 cm and DC = 3 cm, find BC.

$Δ A B D$ is a right triangle right-angled at A and AC \perp BD. Show that
(i) $A B^{2} = B C . B D$
(ii) $A C^{2} = B C . D C$
(iii) $A D^{2} = B D . C D$
(iv) $\frac{A B^{2}}{A C^{2}} = \frac{B D}{D C}$

Q. In a

Δ A B C, A D

is the bisector of

∠ A,

, meeting side

B C

D

.
If

B D = 2 c m, A B = 5 c m

and

D C = 3 c m,

Find

A C

Join BYJU'S Learning Program

Construct an equilateral triangle.ΔABC. Construct an angle bisector of ∠A.Let it meet side BC at D. Find measures of AB,AC,BD,DC.Find the relation between ABAC and BDDC.

The correct option is A ABAC=BDDCIn equilateral triangle ABC,AB = AC.So, ABAC=1Since, angle bisector of ∠A also bisects BC.So, BD = DCHence, BDDC=1Hence, ABAC=BDDCSo, option C is correct.

Construct an equilateral triangle. $Δ A B C$ . Construct an angle bisector of $∠ A$ .
Let it meet side BC at D. Find measures of AB,AC,BD,DC.
Find the relation between $\frac{A B}{A C}$ and $\frac{B D}{D C}$ .

The correct option is A $\frac{A B}{A C}$ $=$ $\frac{B D}{D C}$
In equilateral triangle ABC,
AB = AC.

So, $\frac{A B}{A C} = 1$

Since, angle bisector of $∠ A$ also bisects BC.
So, BD = DC

Hence, $\frac{B D}{D C} = 1$

Hence, $\frac{A B}{A C} = \frac{B D}{D C}$
So, option C is correct.