What you’ll learn
Prove square properties.
Key idea
Equal sides alone prove rhombus; a right angle alone without equal sides is also insufficient for square.
Rhombus alone is insufficient; prove adjacent perpendicularity too.
Worked example
Complete missing statements or reasons in a proof for 'Prove square properties'.
Consecutive coordinate vertices are A=(-2, 1), B=(2, 5), C=(-2, 9), D=(-6, 5). Complete a square proof including both equal-side and right-angle tests.
- all four squared side lengths are 32, and AB dot BC=4*(-4)+4*4=0.
- Four equal sides give a rhombus; the adjacent right angle makes it a square.
Answer: Four equal sides and a right angle — all four squared side lengths are 32, and AB dot BC=4*(-4)+4*4=0.
Quick Check
Complete missing statements or reasons in a proof for 'Prove square properties'.
Consecutive coordinate vertices are A=(2, -1), B=(5, 0), C=(4, 3), D=(1, 2). Complete a square proof including both equal-side and right-angle tests.