Learn to Prove: Kite
Object of Learning
How to prove that a quadrilateral is a kite in two ways: by geometric construction and by deductive reasoning.
Definition
1. A kite is a quadrilateral with two pairs of adjacent sides having equal lengths.
2. Geometric construction is the process of creating geometric shapes using only a compass and a straight edge (ruler) without numerical measurements.
3. Proving by geometric construction involves demonstrating the truth of a geometric statement using a compass and straightedge. These constructions rely on logical deductions and established geometric principles.
4. Proving by deductive reasoning involves proving geometric statements using a logical sequence of steps based on previously accepted facts, definitions, postulates, and theorems
Problem 1
Two circles with centers A and C intersect at D and E. Prove that ACDE is a kite.
Proof by Geometric Construction
The video below shows how to construct a kite.
The construction uses the point tool 
, the line segment tool 
, and the compass tool 
to construct the kite ADCE.
, the line segment tool , and the compass tool to construct the kite ADCE.Practice how to construct a kite.
Proving by deductive reasoning
The series of questions below will give you hints on how to construct the deductive proof. Refer to the figure shown in the video clip, as you may have used different names for the vertices of the kite in your construction.
Is the statement AD=AE true or false?
Which of the following guarantees that AD=AE?
Is this statement CD=CE true or false?
Which of the following justifies that CD=CE?
Is it enough to conclude that AEBD is a kite?
Which of the following statements justifies the conclusion that AECD is a kite?
Problem 2
Circle M and Circle N intersect at points O and T. Prove that quadrilateral MONT is a kite by deductive reasoning.
Statement-Reason form of Deductive Proof
Deductive reasoning can be written in statement-reason form.