objectives: -identify and use the parallel postulate and the triangle sum theorem warm-up: position...
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Objectives:-Identify and use the Parallel Postulate and the Triangle Sum Theorem
3.5 The Triangle Sum Theorem
Warm-Up: Position one letter in each of the five openings. Do this in such a manner that three numbers are spelled out that total thirteen. Words may be written clockwise and counterclockwise, and individual letters may be shared.
The Parallel Postulate: Given a line and a point not on the line, there is one and only one line that contains the given point and is parallel to the given line.
The Triangle Sum Theorem:
The sum of the measures of the angles of a triangle is
Exterior Angle Theorem:
The measure of the exterior angles of a triangle are equal to
Example: Two angle measures are given. Find the missing angle measure or state that the triangle does not exist.
m<1=, m<3=
m<A=, m<C=
m<K_, m<M=
m<X=, m<Z=
Example: Refer to the diagram below, in which DF||BC, AB||FC, m<ADE=, & m<ACB=
m<DBC=
m<CEF=
m<AED=
m<DEC=
m<BDE=
m<DAE=
m<ECF=
A
D
B
E F
C
Example: Find the indicated angle measure.
12
3
πππ ππππ
πππ
Example: Find x and the measure of each angle.
C
(π πβπ)πx =
m<A=
m<B=
m<C=
A
B
(ππ)π
(π π+π)π
Example: Find x and the measure of each angle.
C
(πππβπ)πx =
m<A=
m<B=
m<C=
A
B
(ππ)π
(π π+π)π
Example: Find x and the measure of each angle.
C
(π π)πx =
m<A=
m<B=
m<C=
A
B
(π π )π
Example: Refer to the diagram below to complete the table.
πππ
2
3π¨ 1 4
π©
πͺ
π<ππ<ππ<π+ππ<ππ<π
πππ
πππ
πππ
πππ
πππ
πππ
πππ
Objectives:-Identify and use Triangle Sum Theorem with algebraic scenarios that require factoring.
3.5 The Triangle Sum Theorem Contβd
Warm-Up:
Travel through this maze totaling exactly 100 points. No passage or intersection may be used more than once. Enter and exit the maze at the designated arrows.
Factoring / Zero Product Property Review:
π₯2+10 π₯+24=0π₯2β16 π₯+60=0
3 π₯2+15π₯β34=745 π₯2β40 π₯+86=51
Example: Find x and the measure of each angle.
Z
(π ππ+ππ )π
x = m<W= m<Y= m<Z=
W
Y
(π π+π)π(βπ ππ+ππ)π
Example:Find x and the measure of each angle.
C
(ππ)π
x = m<A= m<B= m<C=
A
B
(π π+ππ)π(βπ π+ππ)π
Example:Find x and the measure of each angle.
F
(ππ)π
x = m<D= m<E= m<F=
D
E
(βπ π+πππ)π(π ππβπ π+π)π
Example: Find x and the measure of each angle.
C
(πππ )π
x = m<A= m<B= m<C=
A
B
(ππππ)π
(πππ)π
Example: Find x and the measure of each angle.
F
(π ππβππ)π
x = m<D= m<E= m<F=
D
E
(ππ+π π+ππ)π
(π π+π)π