SOLUTION: Suppose that ABC is a triangle in which CA > CB. Construct P between C and A so that CP=CB, and let a = angle CAB and theta = angle CPB. Explain why a < theta, Hence prove that a<

Algebra ->  Formulas -> SOLUTION: Suppose that ABC is a triangle in which CA > CB. Construct P between C and A so that CP=CB, and let a = angle CAB and theta = angle CPB. Explain why a < theta, Hence prove that a<       Log On


   

Question 1113549: Suppose that ABC is a triangle in which CA > CB. Construct P between C and A so that CP=CB, and let a = angle CAB and theta = angle CPB. Explain why a < theta, Hence prove that a< angle CBA
Answer by ikleyn(52802) About Me  (Show Source):
You can put this solution on YOUR website!
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It is a classic Elementary Geometry theorem: 

    If in a triangle two sides are unequal, then the angle opposite to the longer side is greater than the angle opposite to the shorter side.

For the proof see the lesson
    - Angles and sides inequality theorems for triangles, Theorem 1
in this site.


Also, you have this free of charge online textbook on Geometry
    - GEOMETRY - YOUR ONLINE TEXTBOOK
in this site.

The referred lesson is the part of this textbook in the section "Properties of triangles".