Here we will prove that in a rectangle the diagonals are of equal lengths.
Given: PQRS is rectangle in which PQ ∥ SR, PS ∥ QR and ∠PQR = ∠QRP = ∠RSP = ∠SPQ = 90°.
To prove: The diagonals PR and QS are equal.
Proof:
Statement |
Reason |
In ∆PQR and ∆RSP, 1. ∠QPR = ∠SRP |
1. PQ ∥ SR and PR is a transversal. |
2. ∠QRP = ∠SPR |
2. PS ∥ QR and PR is a transversal. |
3. PR = PR |
3. Common side. |
4. ∆PQR ≅ ∆RSP Therefore, PQ = RS and QR = SP |
4. By AAS criterion of congruency. CPCTC |
In ∆SPQ and ∆RQP, 5. SP = QR, PQ = PQ and ∠SPQ = ∠RQP |
5. From Statement 4 and given. |
6. ∆SPQ ≅ ∆RQP, Therefore, QS = PR. (Proved) |
6. By SAS criterion of congruency. CPCTC |
From In a Rectangle the Diagonals are of Equal Lengths to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.