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.

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?

Select all that apply

A
True
B
False
C
Neither true or false

Check my answer (3)

Which of the following guarantees that AD=AE?

Select all that apply

A
They are radii of Circle A, so they must have equal lengths.
B
They are radii of Circle C, so they must have equal lengths.

Check my answer (3)

Is this statement CD=CE true or false?

Select all that apply

A
True
B
False
C
Neither true or false

Check my answer (3)

Which of the following justifies that CD=CE?

Select all that apply

A
They are radii of Circle A, so they must have equal lengths.
B
They are radii of Circle C, so they must have equal lengths.

Check my answer (3)

Is it enough to conclude that AEBD is a kite?

Select all that apply

A
Yes
B
No
C
Hard to say

Check my answer (3)

Which of the following statements justifies the conclusion that AECD is a kite?

Select all that apply

A
The shape AECD looks like a kite.
B
The shape AECD is a quadrilateral
C
The shape AECD has two pairs of equal sides: AE=DC and AD=CE.
D
The shape AECD has two pairs of equal sides: AE=AD and CD=CE.
E
The shape AECD is a kite based on the definition of a kite.

Check my answer (3)

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.

Learn to Prove: Kite

Object of Learning

Definition

Problem 1

Proof by Geometric Construction

Practice how to construct a kite.

Proving by deductive reasoning

Problem 2

Statement-Reason form of Deductive Proof

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