the diagonals of cyclic quadrilateral ABCD are congruent show that AD=BC and seg AB parallel seg CD
Answers
Seg AB is parallel to Seg CD.
and, AD = BC
Step-by-step explanation:
Given,
ABCD is a quadrilateral in which both the diagonals are congruent,where both the diagonal AC and BD intersect each other at O.
Length of OA = Length of OC
and, Length of OB = Length of OD
Since, Both the diagonals are equal in length.
So,
Length of OA = Length of OC = Length of OB = Length of OD
Hence, ΔOAB, ΔOBC,ΔOCD,ΔODA are isosceles triangles.
Also, ∠AOB = ∠BOC = ∠COD = ∠DOA = x
As we know that a complete angle is 360°
So, ∠AOB + ∠BOC + ∠COD + ∠DOA = 360°
x+x+x+x=360°
4x = 360°
x= \frac{360}{4}
4
360
= 90°
⇒∠AOB = ∠BOC = ∠COD = ∠DOA = 90°
Also,it is concluded that the all sides of quadrilateral are equal.
So, the given quadrilateral is a square.
⇒ AD = BC = AB =CD
∴, Seg AB is parallel to seg CD.
Answer:
Seg AB is parallel to Seg CD.
and, AD = BC
Step-by-step explanation:
Given,
ABCD is a quadrilateral in which both the diagonals are congruent,where both the diagonal AC and BD intersect each other at O.
Length of OA = Length of OC
and, Length of OB = Length of OD
Since, Both the diagonals are equal in length.
So,
Length of OA = Length of OC = Length of OB = Length of OD
Hence, ΔOAB, ΔOBC,ΔOCD,ΔODA are isosceles triangles.
Also, ∠AOB = ∠BOC = ∠COD = ∠DOA = x
As we know that a complete angle is 360°
So, ∠AOB + ∠BOC + ∠COD + ∠DOA = 360°
x+x+x+x=360°
4x = 360°
x= \frac{360}{4}
4
360
= 90°
⇒∠AOB = ∠BOC = ∠COD = ∠DOA = 90°
Also,it is concluded that the all sides of quadrilateral are equal.
So, the given quadrilateral is a square.
⇒ AD = BC = AB =CD
∴, Seg AB is parallel to seg CD