Mathematics for Class 10>Chapter 7 - Triangles>EXERCISE 7.3>Q 4

EASY

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IMPORTANT

Earn 100

If the median of a triangle are bisectors of the corresponding angles of the triangle, prove that the triangle ie equilateral.

Important Questions on Triangles

EASY

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IMPORTANT

Mathematics for Class 10>Chapter 7 - Triangles>EXERCISE 7.3>Q 5

The bisectors of the

∴ A B = A C . . . . . (i i)

and

∠ C

of a triangle

A B C

meet the opposite sides at

D

and

E

respectively. If

E D ∥ B C

, prove that the triangle is isosceles.

EASY

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IMPORTANT

Mathematics for Class 10>Chapter 7 - Triangles>EXERCISE 7.4>Q 1

If two triangles are similar, prove that the corresponding medians are proportional.

EASY

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IMPORTANT

Mathematics for Class 10>Chapter 7 - Triangles>EXERCISE 7.4>Q 1

If two triangles are similar, prove that the corresponding altitudes are proportional.

EASY

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IMPORTANT

Mathematics for Class 10>Chapter 7 - Triangles>EXERCISE 7.4>Q 2

A B C D

is a parallelogram and

E

is the midpoint of

A B

. If

F

is the point of intersection of

\overset{\leftrightarrow}{D E}

and line

\overset{\leftrightarrow}{B E}

. Prove that

B C = B F

.

EASY

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IMPORTANT

Mathematics for Class 10>Chapter 7 - Triangles>EXERCISE 7.4>Q 3

A B C

is an isosceles triangle in which

A B = A C

and

D

is a point on

A C

such that

B C^{2} = A C \times C D

. Prove that

B C = B D

.

MEDIUM

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IMPORTANT

Mathematics for Class 10>Chapter 7 - Triangles>EXERCISE 7.4>Q 4

If in a triangle

A B C

,

A D ⊥ B C

and

A D^{2} = B D \times D C

, prove that

∠ B A C = 90 °

EASY

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IMPORTANT

Mathematics for Class 10>Chapter 7 - Triangles>EXERCISE 7.4>Q 5

Find the height of a vertical tower which casts a shadow of length

36 m

at the time when the shadow of a vertical post of length

5 m

is

3 m

.

HARD

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IMPORTANT

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

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.