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

𝟒𝟎𝟎 𝟏𝟒𝟎𝟎

𝟔𝟎𝟎

Example: Find x and the measure of each angle.

C

(𝟗 𝒙−𝟒)𝟎x =

m<A=

m<B=

m<C=

A

B

(𝟖𝟔)𝟎

(𝟕 𝒙+𝟐)𝟎

Example: Find x and the measure of each angle.

C

(𝟏𝟏𝒙−𝟕)𝟎x =

m<A=

m<B=

m<C=

A

B

(𝟕𝟓)𝟎

(𝟒 𝒙+𝟕)𝟎

Example: Find x and the measure of each angle.

C

(𝟓 𝒙)𝟎x =

m<A=

m<B=

m<C=

A

B

(𝟒 𝒙 )𝟎

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.

Factoring / Zero Product Property Review:

𝑥2+10 𝑥+24=0𝑥2−16 𝑥+60=0

3 𝑥2+15𝑥−34=745 𝑥2−40 𝑥+86=51

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.

C

(𝒙𝟐)𝟎

x = m<A= m<B= m<C=

A

B

(𝟒 𝒙+𝟓𝟐)𝟎(−𝟑 𝒙+𝟑𝟖)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

Example: Find x and the measure of each angle.

C

(𝟒𝟎𝒙 )𝟎

x = m<A= m<B= m<C=

A

B

(𝟏𝟎𝒙𝟐)𝟎

(𝟑𝟎𝒙)𝟎

Example: Find x and the measure of each angle.

F

(𝟒 𝒙𝟐−𝟏𝟎)𝟎

x = m<D= m<E= m<F=

D

E

(𝒙𝟐+𝟐 𝒙+𝟏𝟎)𝟎

(𝟖 𝒙+𝟓)𝟎