You visited us 3 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

Two Triangles Having the Same Base & Equal Areas

ABC is a tria...

Question

ABC is a triangle with DE $∥$ BC Prove that triangle ABE and triangle ACD are equal in area

Open in App

Solution

In the figure,
$△ B C D$ and $△ B C E$ are between same parallel and same base.

So, Area of $△ B C D =$ Area of $△ B C E$ ........ (1)

Now,
Area of $△ A B C =$ Area of $△ A B C$ ........ (2)

From equation (1) and (2), we get
Area of $△ A B C -$ Area of $△ B C D =$ Area of $△ A B C -$ Area of $△ B C E$
Area of $△ A C D =$ Area of $△ A B E$

Hence, proved.

Suggest Corrections

Similar questions

Q. In the figure D, E are points on the sides AB and AC respectively of

△

ABC such that

a r e a (△ D B C) = a r e a (△ E B C)

. Prove that DE || BC.

D and E are points on the sides AB and AC, respectively, of $△$ ABC such that DE || BC and DE divides $△$ ABC into two parts that are equal in area. Find $\frac{B D}{A B}$ .

Q. In given figure,

A B ⊥ B C

and

D E ⊥ A C

. Prove that

△ A B C \sim △ A E D

Q. In the given figure,

A B

and

D E

are perpendicular to

B C

.
(i) Prove that

△ A B C \sim △ D E C

(ii) If

A B = 6 c m : D E = 4 c m

and

A C = 15 c m

, calculate

C D

.
(iii) Find the ratio of the area of

△ A B C

: area of

△ D E C

Q. In

△ A B C

, if AD is the bisector of

∠ A

, prove that

\frac{A r e a (△ A B D)}{A r e a (△ A C D)} = \frac{A B}{A C}

Join BYJU'S Learning Program

ABC is a triangle with DE ∥ BC Prove that triangle ABE and triangle ACD are equal in area

ABC is a triangle with DE $∥$ BC Prove that triangle ABE and triangle ACD are equal in area