Answer:
A rectangle has congruent diagonals
Step-by-step explanation:
* Lets explain how to solve the problem
- In any rectangle each two opposite sides are parallel and equal
- All the angles of a rectangles are right angles
- To prove that the diagonals of a rectangle are congruent, we will use
the SAS case of congruent
- SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and
including angle in the 2nd Δ
* Lets solve the problem
∵ ABCD is a rectangle
∴ AD = BC
∴ AB = CD
∴ m∠A = m∠B = m∠C = m∠D = 90°
∵ AC and BD are the diagonals of the rectangle
- In the 2 triangles ADC and BCD
∵ AD = BC ⇒ opposite sides in a rectangle
∵ m∠ADC = m∠BCD ⇒ all angles are equal in the rectangle
∵ DC = CD ⇒ common side in the two triangles
∴ ΔADC ≅ ΔBCD ⇒ SAS
- From congruent
∴ AC = BD
∵ AC and BD are the diagonals of the rectangle
∴ The diagonals of the rectangle are congruent
* A rectangle has congruent diagonals
