Table of Contents
- 1 How do you prove ABCD is a kite?
- 2 How are the diagonals of a kite related?
- 3 How do you find the diagonals of a kite?
- 4 What is the perpendicular bisector in kite ABCD?
- 5 What is perpendicular bisector of a kite?
- 6 How do you prove that ABCD is a parallelogram?
- 7 Which angle bisects angles BAD and BCD?
- 8 What is the intersection of line AC and line BD?
- 9 How to prove triangle ABC is congruent?
How do you prove ABCD is 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).
The diagonals of a kite are perpendicular to each other. The longer diagonal of the kite bisects the shorter diagonal. The area of a kite is equal to half of the product of the length of its diagonals.
How do you find the diagonals of a kite?
Explanation: In order to solve this problem, first observe that the red diagonal line divides the kite into two triangles that each have side lengths of and. Notice, the hypotenuse of the interior triangle is the red diagonal. Therefore, use the Pythagorean theorem: , where the length of the red diagonal.
What is the missing reason in step 5 Given ABCD is a kite?
What is the missing reason in step 5? Kite ABCD represents a softball field that is being built.
How can you identify a kite?
It soars with wings bowed and not raised in a ‘V’. Its tail is long and deeply forked when closed and triangular with sharp outer corners, more pronounced in adults when spread. The tail appears pale looking from beneath and is constantly twisting in flight.
What is the perpendicular bisector in kite ABCD?
Kite Properties. Given ABCD a kite, with AB = AD and CB = CD, the following things are true. Diagonal line AC is the perpendicular bisector of BD. The intersection E of line AC and line BD is the midpoint of BD.
What is perpendicular bisector of a kite?
The longer diagonal of a kite is called the main diagonal and the shorter one is called the cross diagonal. The main diagonal of a kite is the perpendicular bisector of the cross diagonal. That is, here the diagonal ¯BD perpendicularly bisects the diagonal ¯AC.
How do you prove that ABCD is a parallelogram?
triangles are congruent. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. If — AB ≅ — CD and — BC ≅ — DA , then ABCD is a parallelogram. If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
What are bisecting diagonals?
In any parallelogram, the diagonals (lines linking opposite corners) bisect each other. That is, each diagonal cuts the other into two equal parts.
Is the quadrilateral ABCD a kite?
Prove: ΔAED ≅ ΔCED It is given that quadrilateral ABCD is a kite. We know that line AD ≅ line CD by the definition of (1)_____. By the kite diagonal theorem, line AC is (2)_____ to line BD This means that angles AED and CED are right angles.
Which angle bisects angles BAD and BCD?
Line AC bisects angles BAD and BCD. Two statements are in bold type, because those statements include the others, from the definitions or perpendicular bisector and congruence of triangles. (Of course to prove the bold statements, one may have to prove some of the others first.
What is the intersection of line AC and line BD?
The intersection E of line AC and line BD is the midpoint of BD. Angles AED, DEC, CED, BEA are right angles. Triangle ABC is congruent to triangle ADC. Consequently angle ABC = angle ADC. Line AC bisects angles BAD and BCD.
How to prove triangle ABC is congruent?
Given a kite ABCD with AB = AD and CB = CD, then triangle ABC is congruent