Question

theorem of cycle quadratic

Answer 1

Answer:

Statements

Reasons

1) ∠ACB = ∠ADB 1) Angles in the same segment.

2) ∠BAC = ∠BDC 2) Angles in the same segment

3)∠ACB + ∠BAC = ∠ADB + ∠BDC 3) Addition property

4) ∠ACB + ∠BAC = ∠ADC 4) Add ∠ABC on both sides.

5) ∠ABC + ∠ACB + ∠BAC = ∠ABC + ∠ADC 5) From Above.

6) 180o = ∠ABC + ∠ADC 6) Sum of the angle of a triangle is 180o

7) ∠B + ∠D = 180o 7) Opposite angles of cyclic quadrilateral.

8) ∠A + ∠B + ∠C + ∠D 8) Measure of a quadrilateral.

9) ∠A + ∠C = 360o - (∠B + ∠D) 9) From Above.

10) ∠A + ∠C = 360o - 180o = 180o 10) Angle sum property

11) ∠A + ∠C = 180o and ∠B + ∠D = 180o 11) From above .So opposite angles are supplementary.

2) If one side of a cyclic quadrilateral is produced, then the exterior angle is equal to the interior opposite angle.

Given : A cyclic quadrilateral ABCD one of whose side AB is produced to E.

Prove that : ∠CBE = ∠ADC

Statements

Reasons

1) ∠ABC + ∠ADC = 180o 1) Opposite angles of cyclic quadrilateral

2) ∠ABC + ∠CBE = 180o 2) Linear Pair angles.

3) ∠ABC + ∠ADC = ∠ABC + ∠CBE 3) From above.

4) ∠ADC = ∠CBE 4) subtraction property