#Properties of a kite bisector free#

Saddle up, because this proof might be a bit of a doozy. Prove that the main diagonal of a kite is the perpendicular bisector of the kite's cross diagonal. Of course, that's where geometry and celebrities differ: Cher did not cut Sonny in half, despite whatever any conspiracy theory might claim. In other words, the main diagonal is perpendicular bisector of the cross diagonal. Since the main diagonal is a line of symmetry, the cross diagonal must be cut in half by the main diagonal.

#Properties of a kite bisector free#

So even with their free spirits and lack of order, there's simply no escaping those right angles.Īnd the patterns don't end there. But these diagonals can do more than sing a killer duet of ' I Got You Babe.' They've actually got some pretty nifty properties too.įor example, the diagonals of a kite are always perpendicular. The cross diagonal is the smaller of the two diagonals (the 'Sonny' of the two), and it doesn't necessarily involve any symmetry. It's the diagonal that's also the kite's line of symmetry. The main diagonal is the larger of the two diagonals (the 'Cher' diagonal, obviously). We'll call them the main diagonal and the cross diagonal (but you can call them Sonny and Cher if you want). Because of this special type of property involving the diagonals, each of the diagonals gets its own name. They don't have to be symmetric about the other diagonal. In this case, ∠ BAD ≅ ∠ DCB.įrom looking at ABCD, we see that it's symmetric about one of the diagonals. What about the other two angles? If you must know (which you must), the angles that connect two non-congruent sides in a kite are congruent. Sides CD and DA are congruent and share ∠ ADC. If we look at kite ABCD, sides AB and BC are congruent, sharing ∠ ABC. (If they were, we'd be looking at a very specific type of kite: a rhombus.) Note that we're not in Parallelogram Country anymore, so these consecutive congruent sides don't mean that all sides are congruent. What makes a kite different from the rest of the quadrilateral kingdom? A kite is a type of quadrilateral with two pairs of consecutive congruent sides. Ish.Ī kite is shaped just like what comes to mind when you hear the word 'kite.' It might not have have a line with colorful bows attached to the flyer on the ground, but it does have that familiar, flying-in-the-wind kind of shape. Parallel sides? Who needs 'em! Kites are free riders, lone wolves who do whatever they want whenever they want. They aren't crazy, but they certainly don't play by the same rules that squares and parallelograms do. Basically, they've descended into anarchy. They don't even have parallel sides like parallelograms. They don't have the nice right angles of squares and rectangles or the equilateral sides of rhombi. There are a couple more families of quadrilaterals that don't really fit inside any nice box. That's all of the major quadrilaterals, right? Uh.not so much.