CK-12 Geometry-Concepts

http://www.ck12.org Chapter 4. Triangles and Congruence

4.5 Third Angle Theorem http://www.ck12.org Contents

Here you’ll learn the Third Angle Theorem and how to use it to determine information about two triangles with two
pairs of angles that are congruent.

What if you were given 4 F GHand 4 XY Zand you were told that^6 F∼=^6 Xand^6 G∼=^6 Y? What conclusion could
you draw about^6 Hand^6 Z? After completing this Concept, you’ll be able to make such a conclusion.

Watch This

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CK-12 Foundation: Chapter4TheThirdAngleTheoremA

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Guidance

Findm^6 Candm^6 J.

The sum of the angles in each triangle is 180◦by the Triangle Sum Theorem. So, for 4 ABC, 35 ◦+ 88 ◦+m^6 C= 180 ◦
andm^6 C= 57 ◦. For 4 HIJ, 35◦+ 88 ◦+m^6 J= 180 ◦andm^6 Jis also 57◦.

Notice that we were given thatm^6 A=m^6 Handm^6 B=m^6 Iand we found out thatm^6 C=m^6 J. This can be
generalized into the Third Angle Theorem.