CameraIcon

SearchIcon

MyQuestionIcon

3

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

Congruent Figures

D is the mid ...

Question

D is the mid point of the base BC of a triangle ABC. DM and DN are perpendiculars on AB and AC respectively. If $D M = D N$ , the triangle is

A

Isosceles

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

B

Equilateral

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

C

Right angled

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

D

Scalene

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

Open in App

Solution

The correct option is B Isosceles
Given: D is mid point of BC. $D M ⊥ A B$ and $D N ⊥ A C$ , $D M = D N$
Now, In $△ D M B$ and $△ D N C$ ,
$D M = D N$ (Given)
$∠ D M B = ∠ D N C$ (Each $90^{\circ}$ )
$B D = D C$ (D is mid point of BC)
Thus, $△ D M B ≅ △ D N C$ (SAS rule)
Thus, $∠ B = ∠ C$ (By cpct)
hence, $△ A B C$ is an Isosceles triangle.

Suggest Corrections

thumbs-up

0

Similar questions

Q. D is the mid-point of the base BC of triangle ABC. DM and DN are perpendiculars on AB and AC respectively. If DM = DN, then the triangle is

D

is a point on hypotenuse

A C

△ A B C

B D ⊥ A C, D M ⊥ B C

D N ⊥ A B .

Prove that :
(i)

D M^{2} = D N . M C

D N^{2} = D M . A N

A B C

be a triangle with

∠ C = 90^{\circ}

C D

perpendicular to

A B

M

N

A C

B C

respectively such that

D M

B C

D N

A C

D M = 5, D N = 4

A C

B C

are respectively equal to

Q. In given figure, ABC is a right triangle right angled at B and D is the foot of the perpendicular drawn from B on AC. If

D M ⊥ B C

D N ⊥ A B

{D M}^{2} = D N \times M C

{D N}^{2} = D M \times A N

D

is a point on hypotenuse

A C

△ A B C

B D ⊥ A C

D M ⊥ B C

D N ⊥ A B

. Prove that:
(i)

{D M}^{2} = D N . M C

{D N}^{2} = D M . A N

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Congruent Figures

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Congruent Figures

Standard VII Mathematics

Join BYJU'S Learning Program

CrossIcon