Secondary 2
Chapter 7
Chapter 7: Properties of Quadrilaterals
7.1/7.2/7.3 - Squares, Rectangles, Parallelograms, Rhombi, Kites & Trapezoids
The Perpendicular/Parallel Line Theorem states: “If two lines are perpendicular to the same line,
then the two lines are parallel to each other.”
Use the given statements and the Perpendicular/Parallel Line Theorem to identify the pair of parallel
lines in each figure.
A square is a quadrilateral with four right angles and all sides congruent.
Example 1: Draw a square with two diagonals. Label the vertices and the intersection of the diagonals.
List all of the properties you know to be true.
A rectangle is a quadrilateral with opposite sides congruent and all angles congruent.
Example 2: Draw a rectangle with two diagonals. Label the vertices and the intersection of the two
diagonals. List all of the properties you know to be true.
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Secondary 2
Chapter 7
A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
Example 3: Draw a parallelogram with two diagonals. Label the vertices and the intersection of the
diagonals. List all of the properties you know to be true.
The Parallelogram/Congruent-Parallel Side Theorem states: “If one pair of opposite sides of a
quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.”
A rhombus is a quadrilateral with all sides congruent.
Example 4: Draw a rhombus with two diagonals. Label the vertices and the intersection of the two
diagonals. List all of the properties you know to be true.
Example 5: Consider the Ace of Diamonds playing card shown. The large diamond in the center of the
playing card is a quadrilateral. Classify the quadrilateral based only on each piece of given information.
a. The diagonals of the quadrilateral bisect each other.
b. The four sides of the quadrilateral are congruent.
c. The four angles and the four sides of the quadrilateral are congruent.
d. The diagonals of the quadrilateral bisect the vertex angles.
e. The four angles of the quadrilateral are congruent
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Secondary 2
Chapter 7
f. The opposite sides of the quadrilateral are both congruent and parallel.
g. The opposite angles of the quadrilateral are congruent
h. The diagonals of the quadrilateral are perpendicular to each other.
i. The diagonals of the quadrilateral are congruent.
A kite is a quadrilateral with two pairs of consecutive congruent sides with opposite sides that are not
congruent.
Example 6: Draw a kite with two diagonals. Label the vertices and the intersection of the two diagonals.
List all of the properties you know to be true.
A trapezoid is a quadrilateral with exactly one pair of parallel sides. The bases of a trapezoid are its
parallel sides. The base angles of a trapezoid are either pair of angles that share a base as a common
side. The legs of a trapezoid are its non-parallel sides.
Example 7: Draw a trapezoid. Identify the vertices, bases, base angles, and legs.
An isosceles trapezoid is a trapezoid with congruent non-parallel sides and congruent base angles.
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