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Theorem 8.4 - Chapter 8 Class 9 Quadrilaterals
Last updated at Dec. 16, 2024 by Teachoo
Opposite angles of parallelogram
Chapter 8 Class 9 Quadrilaterals
Concept wise
- Previous topics
- Definitions
- Opposite sides of parallelogram
-
Opposite angles of parallelogram
- Diagonal of parallelogram
- Theorem 8.8
- Mid point theorem
Transcript
Theorem 8.4: In a parallelogram, opposite angles are equal Given: A parallelogram ABCD with AC as its diagonal To prove: ∠ A = ∠ C & ∠ B = ∠ D Proof: Opposite sides of parallelogram is parallel So, AB ∥ DC and AD‖∥ BC Adding (1) and (2) ∠BAC + ∠DAC = ∠DCA + ∠ BCA ∠BAD = ∠DCB Similarly, we can prove ∠ADC = ∠ABC Hence Proved.
