...Prove that a triangle cannot have more than one right angle. THEOREM V. 76. Each exterior angle pf a triangle is equal to the sum of the two interior and opposite angles. Hypothesis. A BC, any triangle. D, any point on AB produced. Conclusion. Exterior angle CBD = angle...

...is one third of two right angles, or two thirds of one right angle. PROPOSITION XXII. THEOREM. 105. The exterior angle of a triangle is equal to the sum of the two opposite interior angles. л— — Let BC H be an exterior angle of the triangle ABC. We are...

...angles are equal 37 64. The sum of the three angles of a triangle is equal to two right angles 37 68. The exterior angle of a triangle is equal to the sum of its two interior opposite angles ........ 38 69. One angle of an isosceles triangle determines the...

...formed by any side with its adjacent side produced, as CBD, Fig. 116. PROPOSITION IV. Theorem.— Any exterior angle of a triangle is equal to the sum of the two interior non-adjacent angles. DEMONSTRATION. Let ABC be a triangle, and CBD be an exterior angle. We are to...

...produced sides. Let the bisectors of E and F intersect at right angles at О ; then, from the fact that the exterior angle of a triangle is equal to the sum of the interior and opposite angles, if R ba written for a right angle, LA = E + (2 R - D), ¿A=F + (2R...

...can be obtained very simply by geometry. The propositions necessary to prove it are the following: 1. The exterior angle of a triangle is equal to the sum of the opposite interior angles. 2. Two angles are equal when their sides are mutually perpendicular....

...Fio. 21. The other form into which our proposition may be thrown is that either of the exterior angles of a triangle is equal to the sum of the two interior angles opposite to it. For, in the figure, the exterior angle A c D, together with A c B, makes two...

...= half 2^ at center standing on (arc BC + arc DA). PROOF. Join CD. £ BFC = £ BDC + £ DCA. (173. The exterior angle of a triangle is equal to the sum of the opposite interior angles.) But 2 4 BDC = £ at center on BC, and 2 £ DCA = £ at center on DA...

...BFC = half 4 at center standing on (arc BC + arc DA). PROOF. Join CD. 4 BFC = 4 BDC + 4 DCA. (173. The exterior angle of a triangle is equal to the sum of the opposite interior angles.) But 2 4 BDC = 4 at center on BC, and 2 4 DCA = 4 at center on DA ; (375-...

...is onethird of two right angles, or two-thirds of one right angle. PROPOSITION XXIV. THEOREM. 145. The exterior angle of a triangle is equal to the sum of the two opposite interior angles. A c Let BCH be an exterior angle of the triangle ABC. To prove Z...