Download Math 366 Lecture Notes Section 12.2 – Other Congruence Properties

Section 12-2
Math 366 Lecture Notes
Section 12.2 – Other Congruence Properties
Theorem 12-6
Angle, Side, Angle (ASA)
If two angles and the included side of one triangle are congruent to two angles and the included
side of another triangle, respectively then the triangles are congruent.
Theorem 12-7
Angle, Angle, Side (AAS)
If two angles and a corresponding side of one triangle are congruent to two angles and a
corresponding side of another triangle, respectively, then the two triangles are congruent.
Prove the opposite sides of a parallelogram are congruent.
D
A
C
B
Prove the opposite angles of a parallelogram are congruent.
D
A
C
B
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Section 12-2
Prove the diagonals of a parallelogram bisect each other.
D
C
A
B
A median is a segment connecting a vertex to the midpoint of the opposite side of a triangle.
Prove that the median to the hypotenuse in a right triangle is half as long as the hypotenuse.
A
D
B
C
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Section 12-2
Properties of Quadrilaterals
Quadrilateral and Its Definition
A
B
D
Properties of the Quadrilateral
Consecutive angles between parallel sides are
supplementary.
C
Trapezoid: A quadrilateral with at
least one pair of parallel sides
D
C
a.
b.
c.
d.
A parallelogram has all the properties of a trapezoid.
Opposite sides are congruent.
Opposite angles are congruent.
Diagonals bisect each other.
B
A
Parallelogram: A quadrilateral in
which each pair of opposite sides is
parallel
D
C
A
B
Rectangle: A parallelogram with a
right angle.
D
C
A
B
a. A rectangle has all the properties of a parallelogram.
b. All the angles of a rectangle are right angles.
c. A quadrilateral in which all the angles are right
angles is a rectangle.
d. The diagonals of a rectangle are congruent and
bisect each other.
a. Lines containing the diagonals are perpendicular to
each other.
b. A line containing one diagonal is a bisector of the
other.
c. One diagonal bisects nonconsecutive angles.
Kite: A quadrilateral with two
distinct pairs of congruent adjacent
sides
D
A
C
B
Rhombus: A parallelogram with
all sides congruent.
D
C
A
B
a. A rhombus has all the properties of a parallelogram
and a kite.
b. A quadrilateral in which all the sides are congruent
is a rhombus.
c. The diagonals of a rhombus are perpendicular to and
bisect each other.
d. Each diagonal bisects opposite angles.
A square has all the properties of a parallelogram, a
rectangle, and a rhombus.
Square: A rectangle with all sides
congruent
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