Answer:
Sides, angles, and vertices that are next to each other in a polygon are called consecutive.
For example, in the quadrilateral below:
¯¯¯¯¯¯¯¯
A
B
and
C
are consecutive sides
(Note that consecutive sides intersect at a single point.)
∠
D
are consecutive angles
are consecutive vertices
a quadrilateral
When a quadrilateral is named, recall that the vertices are always listed in a consecutive order.
Therefore, the quadrilateral above could be named
or
, but not
.
In a polygon, objects that are not consecutive are said to be nonconsecutive.
In a quadrilateral, nonconsecutive objects are given a special name—they are said to be opposite.
For example, in the quadrilateral above:
¯¯¯¯¯¯¯¯¯
are opposite sides
are opposite angles
are opposite vertices
DEFINITION diagonal
A diagonal of a polygon is a line segment that connects any two nonconsecutive vertices.
Every quadrilateral has two diagonals.
A diagonal of a quadrilateral separates the quadrilateral into two triangles, as shown below:
a diagonal in a quadrilateral
By using the fact that the angles in a triangle sum to 180°, we thus have the following:
THEOREM
The sum of the interior angles in a quadrilateral is 360°.
It follows immediately that if a quadrilateral has four equal angles, then they must each be 90°.
There are several important types of quadrilaterals, which are classified according to extra properti
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Answers & Comments
Answer:
Sides, angles, and vertices that are next to each other in a polygon are called consecutive.
For example, in the quadrilateral below:
¯¯¯¯¯¯¯¯
A
B
and
¯¯¯¯¯¯¯¯
B
C
are consecutive sides
(Note that consecutive sides intersect at a single point.)
∠
C
and
∠
D
are consecutive angles
A
and
D
are consecutive vertices
a quadrilateral
When a quadrilateral is named, recall that the vertices are always listed in a consecutive order.
Therefore, the quadrilateral above could be named
A
B
C
D
or
B
C
D
A
, but not
A
C
B
D
.
In a polygon, objects that are not consecutive are said to be nonconsecutive.
In a quadrilateral, nonconsecutive objects are given a special name—they are said to be opposite.
For example, in the quadrilateral above:
¯¯¯¯¯¯¯¯¯
A
D
and
¯¯¯¯¯¯¯¯
B
C
are opposite sides
∠
B
and
∠
D
are opposite angles
A
and
C
are opposite vertices
DEFINITION diagonal
A diagonal of a polygon is a line segment that connects any two nonconsecutive vertices.
Every quadrilateral has two diagonals.
A diagonal of a quadrilateral separates the quadrilateral into two triangles, as shown below:
a diagonal in a quadrilateral
By using the fact that the angles in a triangle sum to 180°, we thus have the following:
THEOREM
The sum of the interior angles in a quadrilateral is 360°.
It follows immediately that if a quadrilateral has four equal angles, then they must each be 90°.
There are several important types of quadrilaterals, which are classified according to extra properti