In the given figure L M ∥ C B and L N ∥ C D . Prove that A M A B = A N A D .

Given L M ∥ C B and L N ∥ C D . We have to prove A M A B = A N A D . In Δ A C B , we have L M ∥ C B . We know that line drawn parallel to one side of the triangle, intersects the other two sides in distinct points, then it divides the other two sides in same ratio. So, we get, A L L C = A M M B ----(i) Similarly, in Δ A C D , we have L N ∥ C D . So, we get, A L L C = A N N D -----(ii) From (i) and (ii), we get, A M M B = A N N D ⇒ M B A M = N D A N ⇒ M B A M + 1 = N D A N + 1 [adding 1 on both sides] ⇒ M B + A M A M = N D + A N A N ⇒ A B A M = A D A N ⇒ A M A B = A N A D . Hence, proved.

In the given figure, D E ∥ A C and D F ∥ A E . Prove that B F F E = B E E C .

Given D E ∥ A C and D F ∥ A E . We have to prove B F F E = B E E C . We know that if the line drawn parallel to one side of a triangle, intersects the other two sides in distinct points, then it divides the other two sides in same ratio. Here, in Δ A B C , we have D E ∥ A C . So, we get, B E E C = B D D A ----(i) Similarly, in Δ A E B , we have D F ∥ A E . So, we get, B F F E = B D D A ----(ii) From (i) and (ii), we get, ⇒ B F F E = B E E C . Hence, proved.

E M B I B E

Mathematics Class 10>Chapter 8 - Similar Triangles>Exercise

Telangana Board Solutions for Chapter: Similar Triangles, Exercise 4: Exercise

Author:Telangana Board

Telangana Board Mathematics Solutions for Exercise - Telangana Board Solutions for Chapter: Similar Triangles, Exercise 4: Exercise

Attempt the practice questions on Chapter 8: Similar Triangles, Exercise 4: Exercise with hints and solutions to strengthen your understanding. Mathematics Class 10 solutions are prepared by Experienced Embibe Experts.

Questions from Telangana Board Solutions for Chapter: Similar Triangles, Exercise 4: Exercise with Hints & Solutions

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10th Telangana Board

IMPORTANT

Mathematics Class 10>Chapter 8 - Similar Triangles>Exercise>Q 2

In the given figure $L M ∥ C B$ and $L N ∥ C D$ . Prove that $\frac{A M}{A B} = \frac{A N}{A D}$ .

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10th Telangana Board

IMPORTANT

Mathematics Class 10>Chapter 8 - Similar Triangles>Exercise>Q 3

In the given figure, $D E ∥ A C$ and $D F ∥ A E$ . Prove that $\frac{B F}{F E} = \frac{B E}{E C}$ .

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EASY

10th Telangana Board

IMPORTANT

Mathematics Class 10>Chapter 8 - Similar Triangles>Exercise>Q 4

Prove that a line drawn through the midpoint of one side of a triangle parallel to another side bisects the third side. (Using basic proportionality theorem)

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10th Telangana Board

IMPORTANT

Mathematics Class 10>Chapter 8 - Similar Triangles>Exercise>Q 5

Prove that a line joining the midpoints of any two sides of a triangle is parallel to the third side. (Using converse of basic proportionality theorem)

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10th Telangana Board

IMPORTANT

Mathematics Class 10>Chapter 8 - Similar Triangles>Exercise>Q 6

In the given figure, $D E ∥ O Q$ and $D F ∥ O R$ . Show that $E F ∥ Q R$ .

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10th Telangana Board

IMPORTANT

Mathematics Class 10>Chapter 8 - Similar Triangles>Exercise>Q 7

In the given figure, $A, B$ and $C$ are points on $O P, O Q$ and $O R$ , respectively such that $A B ‖ P Q$ and $A C ‖ P R$ . Show that $B C ‖ Q R .$

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10th Telangana Board

IMPORTANT

Mathematics Class 10>Chapter 8 - Similar Triangles>Exercise>Q 8

$A B C D$ is a trapezium in which $A B ∥ D C$ and its diagonals intersect each other at point $' O' .$ Show that $\frac{A O}{B O} = \frac{C O}{D O}$ .