diagonals Archives – Mathemafia http://sh016.global.temp.domains/~mathemaf/tag/diagonals/ Mathematics is like music - Enjoy it!!! Thu, 03 Sep 2020 11:53:22 +0000 en-US hourly 1 https://wordpress.org/?v=7.1.3 https://mathemafia.com/wp-content/uploads/2020/08/cropped-M__Logo__SM-1-32x32.png diagonals Archives – Mathemafia http://sh016.global.temp.domains/~mathemaf/tag/diagonals/ 32 32 Class 9 | Chapter 10 | Circles | Exercise 10.5 | Question 7 https://mathemafia.com/class-9-chapter-10-circles-exercise-10-5-question-7/ Thu, 03 Sep 2020 02:45:40 +0000 http://sh016.global.temp.domains/~mathemaf/?p=1599 Question 7: If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle. Question 6 Question 8 Prerequisite This question has been solved by two different methods –…

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Question 7: If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.

Question 6
Question 8

Prerequisite

This question has been solved by two different methods – both are equally easy to use.

  • Using properties of circle
  • Using SAS triangles congruence

Angle in a semicircle is a right angle

 

Also, following theorem has been discussed as an alternative to prove one of the sections of this question.

Theorem 10.11: The sum of either pair of opposite angles of a cyclic quadrilateral is 180 degree.

 

The other approach used to solve this method is the SAS congruence rule for triangles. It is highly recommended that you must know about the different congruence postulates. These are quite frequently used in geometry. In the following video tutorial, different types of congruence postulates (axioms) are explained along with the difference between congruence and similarity.

Congruence v/s Similarity

Chapter 10 – Circles

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Theorems

Theorem 10.1

Theorem 10.2

Theorem 10.3

Theorem 10.4

Theorem 10.5

Theorem 10.6

Theorem 10.7

Theorem 10.8

Theorem 10.9

Theorem 10.10

Theorem 10.11

Theorem 10.12

Exercise 10.1

Question 1 & 2

Exercise 10.2

Question 1

Question 2

Exercise 10.3

Question 1

Question 2

Question 3

Exercise 10.4

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Exercise 10.5

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Examples

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

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