Mathematics for Class 10>Chapter 7 - Triangles>EXERCISE 7.4>Q 6

HARD

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IMPORTANT

Earn 100

Prove that the line segment joining the midpoints of the sides of a triangle from four triangles, each of which is similar to the original triangle.

Important Questions on Triangles

EASY

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IMPORTANT

Mathematics for Class 10>Chapter 7 - Triangles>EXERCISE 7.4>Q 7

In triangle

A B C

,

D E

is parallel to base

B C

with

D

on

A B

and

E

on

A C

. If

\frac{A D}{D B} = \frac{2}{3}

, find

\frac{B C}{D E}

.

MEDIUM

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IMPORTANT

Mathematics for Class 10>Chapter 7 - Triangles>EXERCISE 7.4>Q 8

In a

△ A B C

,

P

and

△ A B C ~ △ D E F

are points on

A B

and

A C

respectively such that

P Q ∥ B C

. Prove that median

A D

bisects

P Q

.

EASY

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IMPORTANT

Mathematics for Class 10>Chapter 7 - Triangles>EXERCISE 7.4>Q 9

A B C

is an isosceles triangle in which

A B = A C .

A D

is drawn perpendicular to

B C

. From a point

E

on

C B

produced,

E F

is drawn perpendicular to

A C

. Prove that

△ A D C ~ △ E C F

EASY

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IMPORTANT

Mathematics for Class 10>Chapter 7 - Triangles>EXERCISE 7.4>Q 10

$A B C$ is a right triangle right-angled at $B$ and $D$ is the foot of the perpendicular drawn from $B$ on $A C$ . If $D M ⊥ B C$ and $D N ⊥ A B$ where $M, N$ lie on $B C$ , $A B$ respectively, prove that $D M^{2} = D N \times M C$ .

EASY

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IMPORTANT

Mathematics for Class 10>Chapter 7 - Triangles>EXERCISE 7.4>Q 10

A B C

is a right triangle right-angled at

B

and

D

is the foot of the perpendicular drawn from

B

on

A C

. If

D M ⊥ B C

and

D N ⊥ A B

where

M, N

lie on

B C

,

A B

respectively, prove that

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

.

HARD

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IMPORTANT

Mathematics for Class 10>Chapter 7 - Triangles>EXERCISE 7.4>Q 11

Through the vertex

D

of parallelogram

A B C D

, a line is drawn to intersects the sides

B A

produced and

B C

produced at

E

and

F

respectively. Prove that

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

EASY

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IMPORTANT

Mathematics for Class 10>Chapter 7 - Triangles>EXERCISE 7.4>Q 12

The perimeter of two similar triangle

A B C

and

P Q R

respectively,

72 c m

and

48 c m

. If

P Q = 20 c m

, find

A B

EASY

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IMPORTANT

Mathematics for Class 10>Chapter 7 - Triangles>EXERCISE 7.4>Q 13

Two right triangles

A B C

and

D B C

are drawn on the same hypotenuse

B C

and on the same side of

B C

. If

A C

and

B D

intersects at P

P

, prove that

A P \times P C = P D \times P B