Given: In square ABCD, the points E and F are the midpoints of sides BC and AD respectively.
a
Prove: ΔABF ≅ ΔCDE
Arrange the proof steps in the correct order:
1
2
3
4
Excellent! The proof is correct!
Explanation:
1. AB = CD - because all sides of a square are equal
2. AF = CE - because F is the midpoint of AD and E is the midpoint of BC, so both equal half the side length
3. ∠BAF = ∠DCE = 90° - because all angles in a square are right angles
4. Therefore the triangles are congruent by SAS (Side-Angle-Side)
b
Given that the perimeter of the square is 24 cm. Calculate:
Hint: Side length of the square = perimeter / 4 = 24 / 4 = 6 cm
Area of square ABCD:
cm²
Correct! 6² = 36
Area of triangle ABF:
cm²
Correct! (6 × 3) / 2 = 9
Full solution:
• Side of the square: s = 24 / 4 = 6 cm
• Area of the square: s² = 6² = 36 cm²
• AF = AD / 2 = 6 / 2 = 3 cm
• Area of triangle ABF: (AB × AF) / 2 = (6 × 3) / 2 = 9 cm²
Well done! You completed Question 41!
You understood how to prove triangle congruence and calculate areas in a square!