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← elements / Posts tagged 'similar-segments-of-circles'

Posts tagged 'similar-segments-of-circles'

G.127 similar circle segments

Similar segments of circles are those which admit equal:term:angles <G.22>, or in which the angles are equal.
definition plane-geometry circles book-iii similar-segments-of-circles plane-angle similar plane
A B C D

G.128 no two similar unequal circle segments on the same chord

On the same segment and on the same side of it, there cannot be constructed two similar and unequal segments of circles.
theorem proof plane-geometry circles book-iii segment circle angle straight-line segment-of-circle similar-segments-of-circles plane-angle similar equality reductio-ad-absurdum
A B E C D F G

G.129 similar circle segments on equal chords are equal

Similar segments of circles on equal segments are equal to one another.
theorem proof plane-geometry circles book-iii point segment circle similar-segments-of-circles straight-line similar equality coincidence reductio-ad-absurdum
A B C G K D E F H L

G.133 equal angles stand on equal arcs

In equal circles, equal angles stand on equal arcs, whether they stand at the centers or at the circumferences.
theorem proof plane-geometry circles book-iii point segment circle angle equal-circles plane-angle stand-upon-circumference centre straight-line similar-segments-of-circles arc plane equality
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