Class 9 | Chapter 10 | Circles | Exercise 10.5 | Question 12

04 Sep
Class 9 - Circles, , , , , , , ,

Question 12: Prove that a cyclic parallelogram is a rectangle.

Question 11
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Prerequisite

It is commonly said that in mathematics one question can be solved in multiple ways. This question is another good example to prove it. This question has been solved by three different methods by using the following concepts.

  1. Opposite angles of a parallelogram are always congruent
  2. Same side interior angles on two parallel lines are supplementary
  3. Using congruence postulate

Theorem 8.4: In a parallelogram, opposite angles are equal.

 

Theorem 6.4: If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary.

 

Congruence vs. 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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