10. ABCD is a quadrilateral in which P, Q, R and S are midpoints of the sides AB, BC, CD and
DA, AC is a diagonal. Show that PQ = SR
Answers
Answer:-
Given:
- ABCD is a quadrilateral
- P , Q , R and S are the mid - points of sides AB, BC, CD and DA
- AC is a diagonal of quadrilateral
To Prove:
- PQ = SR
Proof:
➥ The Midpoint Theorem states that the line joining two sides of a triangle at the midpoints of those two sides is parallel to the third side and is half the length of the third side.
➣ In △ADC ,
S is the mid point of DA and R is the mid point of DC.
∴ SR || AC and SR= ½ AC-----eq.1 [By mid-point theorem]
➣ In △ACB ,
P is the mid point of AB and Q is the mid point of BC.
∴ PQ || AC and PQ= ½AC-----eq.2 [By mid-point theorem]
➣ But from eq.1 and eq.2
SR = ½AC
PQ = ½ AC
➣ So,
½ AC = SR = PQ
Hence,
It is proved that SR = PQ.
Step-by-step explanation:
✰ Question ⤵
ABCD is a quadrilateral in which P, Q, R and S are midpoints of the sides AB, BC, CD and DA, AC is a diagonal. Show that PQ = SR
✰ Solution ⤵
=> The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.
In △DAC , S is the mid point of DA and R is the mid point of DC.
Therefore, SR ∥ AC and SR= 1/2 AC.
By mid-point theorem.
Hence, it's proved SR = PQ
.
Hope it helpful.. ✌️
