A Treatise On Geometry And Its Application in the Arts

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But B D is equal to A C ; therefore A E is equal to A C. The triangle C A E is therefore isosceles, and the angle A E C is equal to the angle C ; but since A E is parallel to B D, the angle A E C is equal to the angle D ; therefore the angle C must be equal to the angle D, which are the angles that the sides make with the base C D. Again since A B is parallel to C D, the angles BAG and G, as well as B andD, are supplemental (41. ) ; but the angle C has been proved to be equal to the angle D ; t...here- fore the angle G A B is equal to the angle B, which are the angles that the sides make with the base A B.
(150. ) If the angles at the base of a trapezium b6 equal, its sides will be equal.
CHAP. Vr. GEOMETRY. 73 For, let A E ( fig, 70. ) be drawn parallel to B D ; then, as in (149. )) A E will be equal to B D ; but since the angle A E C is equal to the angle D, it is also equal to the angle C, and therefore the triangle C A E is isosceles, and the side C A is equal to the side AE ; but A E has been proved equal to B D, and therefore A C is equal to B D.


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