http://www.ck12.org Chapter 4. Triangles and Congruence
Example A
Determine the measure of the missing angles.
From the markings, we know that^6 A∼=Dand^6 E∼=^6 B. Therefore, the Third Angle Theorem tells us that^6 C∼=^6 F.
So,
m^6 A+m^6 B+m^6 C= 180 ◦
m^6 D+m^6 B+m^6 C= 180 ◦
42 ◦+ 83 ◦+m^6 C= 180 ◦
m^6 C= 55 ◦=m^6 FExample B
The Third Angle Theorem states that if two angles in one triangle are congruent to two angles in another triangle,
then the third pair of angles must also congruent. What additional information would you need to know in order to
be able to determine that the triangles are congruent?
In order for the triangles to be congruent, you need some information about the sides. If you know two pairs of
angles are congruent and at least one pair of corresponding sides are congruent, then the triangles will be congruent.
Example C
Determine the measure of all the angles in the triangle:
First we can see thatm^6 DCA= 15 ◦. This means thatm^6 BAC= 15 ◦also because they are alternate interior angles.
m^6 ABC= 153 ◦was given. This means by the Triangle Sum Theorem thatm^6 BCA= 12 ◦. This means thatm^6 CAD=
12 ◦also because they are alternate interior angles. Finally,m^6 ADC= 153 ◦by the Triangle Sum Theorem.
Watch this video for help with the Examples above.
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter4TheThirdAngleTheoremB
Concept Problem Revisited
For two given triangles 4 F GHand 4 XY Z, you were told that^6 F∼=^6 Xand^6 G∼=^6 Y.
By the Third Angle Theorem,^6 H∼=^6 Z.
Vocabulary
Two figures arecongruentif they have exactly the same size and shape. Two triangles arecongruentif the three
corresponding angles and sides are congruent. TheTriangle Sum Theoremstates that the measure of the three
interior angles of any triangle will add up to 180◦. TheThird Angle Theoremstates that if two angles in one
triangle are congruent to two angles in another triangle, then the third pair of angles must also congruent.