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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.
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: Refer to the diagram below to complete the table.
𝟑𝟎𝟎
2
3𝑨 1 4
𝑩
𝑪
𝒎<𝟏𝒎<𝟐𝒎<𝟏+𝟐𝒎<𝟑𝒎<𝟒
𝟑𝟎𝟎
𝟒𝟎𝟎
𝟒𝟎𝟎
𝟕𝟎𝟎
𝟖𝟎𝟎
𝟖𝟎𝟎
𝟗𝟎𝟎
Objectives:-Identify and use Triangle Sum Theorem with algebraic scenarios that require factoring.
3.5 The Triangle Sum Theorem Cont’d
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.
Example: Find x and the measure of each angle.
Z
(𝟑 𝒙𝟐+𝟓𝟎 )𝟎
x = m<W= m<Y= m<Z=
W
Y
(𝟓 𝒙+𝟗)𝟎(−𝟐 𝒙𝟐+𝟗𝟕)𝟎
Example:Find x and the measure of each angle.
F
(𝒙𝟐)𝟎
x = m<D= m<E= m<F=
D
E
(−𝟗 𝒙+𝟏𝟎𝟎)𝟎(𝟐 𝒙𝟐−𝟔 𝒙+𝟖)𝟎