...^4 + Z JB + Z BOA = 2 right angles. QED B 80. COK. 1. Equation (a) when expressed in words is : ^e exterior angle of a triangle is equal to the sum of the two interior and opposite angles. 81. COR. 2. If two angles of a triangle are given, or merely their sum, the third...

...charcoal diagram on the floor of his play-room, the thirty-second proposition of the first book of Euclid (the exterior angle of a triangle is equal to the sum of the two interior and opposite angles, and the three angles of a triangle together equal two right angles). In secret,...

.../—The determination of these circles depends on the two following propositions of geometry: namely, the exterior angle of a triangle is equal to the sum of the two opposite interior angles; and, secondly, an inscribed angle is measured by one-half the arc...

...rays = Z_ BE 6 ; and .'. Z ab B = 2 Z pb B, and Z&BE = 2Z&BP, FIG. But and - Z &B P = Z &PB because the exterior angle of a triangle is equal to the sum of the interior and opposite angles; instrument, is divided into 10' or 20', and those are subdivided...

...at the second surface, so that D = d+d'. But d = i — r. and d'=V— r', therefore But r + r' = A, (the exterior angle of a triangle is equal to the sum of the two opposite interior angles), where A is equal in magnitude to the angle of the prism (their sides...

...8. // two angles have their sides parallel respectively they are either equal or supplementary. 9. The exterior angle of a triangle is equal to the sum of the two remote interior angles. 11. The consecutive angles of a parallelogram arc supplementary. 217....

...ABC. Give reasons. If a few more exercises of this type are given the children should observe that the exterior angle of a triangle is equal to the sum of the two remote interior angles. 2. Draw a scalene triangle ABD, then draw the line A C. Suppose that...

...Proposition 32, Book 1, proved to lie fallacious (Liverpool, 1870). This is the theorem which asserts that the exterior angle of a triangle is equal to the sum of the two opposite interior angles, and that the sum of the interior angles equals two right angles....

...or supplemental. Theorem XX. The sum of the angles of a triangle is a straight angle. Corollary 1. The exterior angle of a triangle is equal to the sum of the interior angles not adjacent to It. Corollary 2. A triangle can have but one right angle or one...

...straight angle. Z BAC + Z ACB + Z CBA = a straight angle. Why? State the theorem proved. Corollary 1. The exterior angle of a triangle is equal to the sum of the interior angles not adjacent to it. Corollary 3. // two angles of a triangle are equal respectively...