Table of Contents | Introduction | Home P l a n e G e o m e t r y An Adventure in Language and Logic based on VERTICAL ANGLESBook I. Proposition 15WHEN TWO STRAIGHT LINES AB, CD intersect one another, then angles AEC, DEB are called vertical angles (or vertically opposite), as are angles AED, CEB. Those are the two pairs of vertical angles that intersecting straight lines form. Now, angles AEC, AED together are equal to two right angles (Proposition 13), as are angles AEC, CEB. Therefore if we take away angle AEC from each pair -- -- then we can see that angle AED will equal angle CEB. The vertical angles are equal. That is the next theorem. PROPOSITION 15. THEOREM
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