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Kite definition Geometry
You probably understand a kite as that exorbitant toy that paris aloft ~ above the wind, tethered to you by string. That toy kite is based on the geometric shape, the kite.
You are watching: Are the diagonals of a kite congruent
A kite is a quadrilateral form with 2 pairs of surrounding (touching), congruent (equal-length) sides. That way a dragon is all of this:A airplane figureA closed shapeA polygon
Sometimes a kite have the right to be a rhombus (four congruent sides), a dart, or also a square (four congruent sides and also four congruent internal angles).
Some kites are rhombi, darts, and squares. No every rhombus or square is a kite. All darts space kites.
Kites can be convex or concave. A dart is a concave kite. That method two the its sides move inward, toward the within of the shape, and one of the four interior angle is higher than 180°. A dart is also called a chevron or arrowhead.
How To build A kite in Geometry
You can make a kite. Find four uncooked spaghetti strands. Reduced or break two spaghetti strands come be same to every other, but shorter than the various other two strands.
Touch two endpoints the the short strands together. Touch two endpoints the the longer strands together. Currently carefully bring the remaining four endpoints together so an endpoint the each quick piece touch an endpoint that each lengthy piece. You have a kite!
How To draw A kite In Geometry
You can additionally draw a kite. Use a protractor, ruler and also pencil. Attract a line segment (call it KI) and, native endpoint I, draw an additional line segment the same length as KI. That new segment will be IT.
The angle those 2 line segments make (∠I) have the right to be any type of angle other than 180° (a right angle).
Draw a dashed line to connect endpoints K and also T. This is the diagonal line that, eventually, will most likely be inside the kite. Now use her protractor. Line it up along diagonal KT so the 90° mark is at ∠I. Note the clues on diagonal KT where the perpendicular touches; that will certainly be the center of KT.
Lightly draw that perpendicular together a dashed line passing with ∠I and the center of diagonal KT. Make that line as long as friend like.
If you finish the line closer to ∠I than diagonal KT, friend will acquire a dart. If you end the new line more away indigenous ∠I 보다 diagonal KT, you will certainly make a convex kite.
Connect the endpoint of the perpendicular line v endpoint T. Brand it point E. Connect allude E with point K, developing line segment EK. Notification that heat segments (or sides) TE and EK space equal. Notice that sides KI and also IT are equal.
You probably attracted your dragon so sides KI and EK are not equal. The also means IT and also TE space not equal. You could have attracted them all equal, making a rhombus (or a square, if the internal angles are best angles).
Properties the Kites
The kite"s sides, angles, and also diagonals all have actually identifying properties.
To it is in a kite, a quadrilateral must have actually two bag of sides that space equal come one another and also touching. This renders two bag of adjacent, congruent sides.
You could have one pair that congruent, nearby sides however not have a kite. The other two sides might be of unequal lengths. Then you would have only a quadrilateral.
Your kite can have four congruent sides. Her quadrilateral would certainly be a kite (two pairs of adjacent, congruent sides) and a rhombus (four congruent sides).
Where 2 unequal-length sides fulfill in a kite, the interior angle they produce will constantly be same to its the contrary angle. Look at the kite you drew.
∠K = ∠T and ∠I = ∠E.
It is possible to have actually all 4 interior angles equal, making a kite the is additionally a square.
The two diagonals of our kite, KT and IE, crossing at a ideal angle. In every kite, the diagonals intersect at 90°. Occasionally one of those diagonals could be outside the shape; climate you have actually a dart. That does no matter; the intersection of diagonals the a dragon is always a ideal angle.
A second identifying building of the diagonals the kites is that one of the diagonals bisects, or halves, the other diagonal. They can both bisect each other, do a square, or just the much longer one might bisect the much shorter one.
For what appears to be a really straightforward shape, a kite has actually a lot of of exciting features. Utilizing the video and this created lesson, we have learned that a dragon is a quadrilateral with two bag of adjacent, congruent sides.
Kites deserve to be rhombi, darts, or squares. We additionally know that the angles produced by unequal-length sides are constantly congruent.
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Finally, we understand that the kite"s diagonals always cross at a appropriate angle and also one diagonal always bisects the other.
What Is a Rectangle?
What girlfriend learned:
After the town hall the video and analysis this lesson, you will learn to:Recognize the polygon referred to as a kitePlace the kite in the family members of quadrilateralsDefine a kiteKnow the three identifying nature of a kite