In the figure below, A C and B E are parallel lines: Are the length of B C and D E equal? Why?

The angles between any two of the corresponding or similar sides in the two triangles are equal angles. Since A C = B E = 6 cm and A B = B D = 4 cm ⇒ ∠ A C B = B E D By SAS test △ C B A ≃ △ E D B ⇒ B C = D E ( ∵ They are the corresponding sides of two equal triangles) Hence, they are equal.

In the figure below, A C and B E are parallel lines: Are B C and D E parallel? Why?

The angles between any two of the corresponding or similar sides in the two triangles are equal angles. Given A C = B E = 6 cm and A B = B D = 4 cm ⇒ ∠ A C B = B E D By SAS test △ C B A ≃ △ E D B ⇒ B C = D E Hence, B C ∥ D E ( ∵ They are the corresponding sides of two equal triangles)

In the figure below, the lines A B and C D are parallel and M is the midpoint of A B . Compute the angles of △ A M D , △ M B C and △ D C M ?

Given, lines A B and C D are parallel and M is the midpoint of A B . ∠ A M D = ∠ M B C = 60 ° (corresponding angles) ∠ C M B = ∠ D A M = 40 ° (corresponding angles) ∠ C D M = ∠ A M D = 60 ° (alternate interior angles) ∠ D C M = ∠ C M B = 40 ° (alternate interior angles) On straight line A M B , ⇒ ∠ A M D + ∠ D M C + ∠ C M B = 180 ° (angles in a straight line) ⇒ 60 ° + ∠ D M C + 40 ° = 180 ° ⇒ ∠ D M C + 100 ° = 180 ° ⇒ ∠ D M C = 180 ° - 100 ° ⇒ ∠ D M C = 80 ° ⇒ ∠ A D M = ∠ M C B = ∠ D M C = 80 ° (alternate interior angles) Therefore, now we have,

In the figure below, the lines A B and C D are parallel and M is the midpoint of A B . What is special about the quadrilaterals A M C D and M B C D

Given, lines A B and C D are parallel and M is the midpoint of A B . ∠ A M D = ∠ M B C = 60 ° (corresponding angles) ∠ C M B = ∠ D A M = 40 ° (corresponding angles) ∠ C D M = ∠ A M D = 60 ° (alternate interior angles) ∠ D C M = ∠ C M B = 40 ° (alternate interior angles) On straight line A M B , ⇒ ∠ A M D + ∠ D M C + ∠ C M B = 180 ° (angles in a straight line) ⇒ 60 ° + ∠ D M C + 40 ° = 180 ° ⇒ ∠ D M C + 100 ° = 180 ° ⇒ ∠ D M C = 180 ° - 100 ° ⇒ ∠ D M C = 80 ° ⇒ ∠ A D M = ∠ M C B = ∠ D M C = 80 ° (alternate interior angles) Therefore, now we have, From the given figure, △ A M D = △ M B C = △ C M D Quadrilaterals A M C D and M B C D both contain two equal triangles. That is what makes special. Quadrilateral A M C D consists of △ A M D and △ C M D . Quadrilateral M B C D consists of △ M B C and △ C M D .

E M B I B E

Standard 8 Mathematics Part - 1>Chapter 1 - Equal Triangles>Exercise 2

Kerala Board Solutions for Chapter: Equal Triangles, Exercise 2: Exercise 2

Author:Kerala Board

Kerala Board Mathematics Solutions for Exercise - Kerala Board Solutions for Chapter: Equal Triangles, Exercise 2: Exercise 2

Attempt the free practice questions on Chapter 1: Equal Triangles, Exercise 2: Exercise 2 with hints and solutions to strengthen your understanding. Standard 8 Mathematics Part - 1 solutions are prepared by Experienced Embibe Experts.