The diagonals of a quadrilateral A B C D intersect each other at the point O such that A O B O = C O D O . Show that A B C D is a trapezium.

Draw a line segment O E ∥ A B In △ A B C Since, O E ∥ A B . Hence, A O O C = B E E C . But by the given relation, we have: A O B O = C O D O ⇒ A O O C = O B O D Hence, O B O D = B E E C So, using converse of basic proportionality theorem, E O ∥ D C . Therefore, A B ∥ O E ∥ D C ⇒ A B ∥ C D Therefore, A B C D is a trapezium.

E M B I B E

MATHEMATICS Textbook for Class X>Chapter 6 - Triangles>Exercise 6.2>Q 8

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IMPORTANT

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Using the converse of Basic Proportionality Theorem (BPT), prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side.

Important Questions on Triangles

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IMPORTANT

MATHEMATICS Textbook for Class X>Chapter 6 - Triangles>Exercise 6.2>Q 9

A B C D

is a trapezium in which

A B ∥ D C

and its diagonals intersect each other at the point

O

. Show that

\frac{A O}{B O} = \frac{C O}{D O}

HARD

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IMPORTANT

MATHEMATICS Textbook for Class X>Chapter 6 - Triangles>Exercise 6.2>Q 10

The diagonals of a quadrilateral

A B C D

intersect each other at the point

O

such that

\frac{A O}{B O} = \frac{C O}{D O}

. Show that

A B C D

is a trapezium.

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IMPORTANT

MATHEMATICS Textbook for Class X>Chapter 6 - Triangles>Exercise 6.3>Q 1

State which pairs of triangles in the figure are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form:
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IMPORTANT

MATHEMATICS Textbook for Class X>Chapter 6 - Triangles>Exercise 6.3>Q 1

Are the pairs of triangles in the figure similar? Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form:
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IMPORTANT

MATHEMATICS Textbook for Class X>Chapter 6 - Triangles>Exercise 6.3>Q 1

State whether the following pair of triangles is similar or not.

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10th Assam Board

IMPORTANT

MATHEMATICS Textbook for Class X>Chapter 6 - Triangles>Exercise 6.3>Q 1

State if the following pairs of triangles in the figure are similar or not. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form:

Question Image

MEDIUM

10th Assam Board

IMPORTANT

MATHEMATICS Textbook for Class X>Chapter 6 - Triangles>Exercise 6.3>Q 1

State whether the following pair of triangles is similar or not.

Question Image

MEDIUM

10th Assam Board

IMPORTANT

MATHEMATICS Textbook for Class X>Chapter 6 - Triangles>Exercise 6.3>Q 1

State whether the pair triangles are similar or not. Write the similarity criterion used by you for answering the question and also write the pair of similar triangles in the symbolic form.

Question Image

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