MPM 1DI Unit 7
Geometric Relationships
7.2 Angle Relationships in Quadrilaterals
Warm Up:
Determine the value of x and y.
x
y
7.2 Angle Relationships in Quadrilaterals
Common Terms:
Adjacent: adjoining or next to
Complementary: adding to 90 degrees
Supplementary: adding to 180 degrees
Transversal: a line intersecting two parallel lines
Obtuse Angle: angle greater than 90 degrees
Acute Angle: angle less than 90 degrees
Acronyms for Justification
T.P.T. - C.A. - Transversal Parallel Line Theorem
Corresponding Angles (F-pattern)
e.g. A = D (T.P.T - C.A.)
T.P.T. - A.A. - Alternate Angles
(Z-pattern)
e.g.
B=C
(T.P.T.- A.A.)
T.P.T. - C.I.A. - Co-interior Angles (C-pattern)
e.g. E + F = 180o
(T.P.T - C.I.A.)
O.A.T. - Opposite Angle Theorem
e.g.
G=H
(O.A.T.)
S.A.T. - Supplementary Angles Theorem
e.g.
I+J
= 180o
(SAT)
E.A.T. - Exterior Angle Theorem
e.g.
X = Y+Z
(E.A.T.)
P.E.A.S.T - Polygon Exterior Angle Sum
Theorem
(P.E.A.S.T.)
e.g. 360 = X+A+B
A.S.Q.T. - Angle Sum Quadrilateral Theorem
(Or you may just say ...
sum of interior angles of quadrilateral)
A
G
E
B
D F
I
C
J
Y
X
X
H
A
Z
B
QUADRILATERAL:
Find the sum of the interior angles
2. Measure the interior angles.
Draw a line between two non­adjacent rtices (this is called a diagonal).
ce we have created two triangles our quadrilateral.
asure and label the 4 exterior angles, nd their sum.
1. Draw a large quadrilateral (la
Summary:
1. The sum of the interior angles of a quadrilateral is 360 degrees.
A.S.Q.T. - Angle Sum Quadrilateral Theorem
(Or you may just say ...
sum of interior angles of quadrilateral)
2. A+B+C+D
The sum of the exterior angles of a = 360
quadrilateral is 360 degrees. (P.E.A.S.T)
O
W+X+Y+Z = 360O
W
A
B
X
C
Z
D
Y
Examples:
1. Find each of the unknown angles:
120O
a
108O e
75O
b c
d
a = 180o ­ 120o (Supp)
= 60o
(ASQT)
2. Find the measure of each unknown angle:
a
y+10o
(angle 1)
b
2y-30o
y
(angle 2)
c
72o
d
(Substitution)
(Substitution)
(Supp)
(Supp)
(Supp)