One of the two diagonals of a convex kite divides it into two isosceles triangles; the other (the axis of symmetry) divides the kite into two congruent triangles. The two interior angles of a kite that are on opposite sides of the symmetry axis are equal.
What angles are congruent in a kite?
The angles between the congruent sides are called vertex angles. The other angles are called non-vertex angles. If we draw the diagonal through the vertex angles, we would have two congruent triangles. Theorem: The non-vertex angles of a kite are congruent.
Are all sides of a kite congruent?
Geometry For Dummies, 2nd Edition
A kite is a quadrilateral in which two disjoint pairs of consecutive sides are congruent (“disjoint pairs” means that one side can’t be used in both pairs). … The opposite angles at the endpoints of the cross diagonal are congruent (angle J and angle L).
Can a kite have 3 congruent angles?
Kite properties include (1) two pairs of consecutive, congruent sides, (2) congruent non-vertex angles and (3) perpendicular diagonals. Other important polygon properties to be familiar with include trapezoid properties, parallelogram properties, rhombus properties, and rectangle and square properties.
Does a kite have 4 congruent sides?
To be a kite, a quadrilateral must have two pairs of sides that are equal to one another and touching. This makes two pairs of adjacent, congruent sides. … Your kite could have four congruent sides. Your quadrilateral would be a kite (two pairs of adjacent, congruent sides) and a rhombus (four congruent sides).
Are opposite angles equal in a kite?
The two interior angles of a kite that are on opposite sides of the symmetry axis are equal.
How do you prove a kite?
How to Prove that a Quadrilateral Is a Kite
- If two disjoint pairs of consecutive sides of a quadrilateral are congruent, then it’s a kite (reverse of the kite definition).
- If one of the diagonals of a quadrilateral is the perpendicular bisector of the other, then it’s a kite (converse of a property).
Can a kite have 2 right angles?
Thus the right kite is a convex quadrilateral and has two opposite right angles. If there are exactly two right angles, each must be between sides of different lengths. All right kites are bicentric quadrilaterals (quadrilaterals with both a circumcircle and an incircle), since all kites have an incircle.
What is a diagonal of a kite?
The diagonals of a quadrilateral with two pairs of adjacent congruent sides – a kite – are perpendicular; also, bisects the and angles of the kite. Consequently, is a 30-60-90 triangle and is a 45-45-90 triangle.
Is a rhombus a kite?
A kite has two sets of adjacent congruent sides. … This means that all Rhombi are kites, but not all kites are rhombi. A square is a rhombus with all right angles. This means that all squares are rhombi (which means they have to be kites), but not all rhombi are squares.
Does a kite have a right angle?
The intersection of the diagonals of a kite form 90 degree (right) angles. This means that they are perpendicular. The longer diagonal of a kite bisects the shorter one.
What does congruent mean?
Congruent means same shape and same size. So congruent has to do with comparing two figures, and equivalent means two expressions are equal. So to say two line segments are congruent relates to the measures of the two lines are equal.
What are the five properties of kite?
- Opposite sides are parallel and equal in length.
- Opposite angles are equal in measure.
- Adjacent angles sum up to 180 degrees.
- It has 2 diagonals that bisect each other.
- Each diagonal divides the parallelogram into 2 congruent triangles.
Can the diagonals of a kite be congruent?
THEOREM: If a quadrilateral is an isosceles trapezoid, the diagonals are congruent. … THEOREM: If a quadrilateral is a kite, the diagonals are perpendicular. THEOREM: If a quadrilateral is a kite, it has one pair of opposite angles congruent.
Why is a rhombus a kite?
A rhombus is a quadrilateral with all sides of equal length. So a rhombus does have two pairs of adjacent sides of equal length and is therefore a kite.
What does a kite equal?
By definition, a kite is a polygon with four total sides (quadrilateral). The sum of the interior angles of any quadrilateral must equal: degrees degrees degrees. Additionally, kites must have two sets of equivalent adjacent sides & one set of congruent opposite angles.