.../—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...

...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....

...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...

...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....

...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...

...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...

...are equal. COR. III. The acute angles of a right triangle are complements of each other. THEOREM lit. The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. THEOREM 20. The sum of the interior angles of a polygon of n...

...triangle bisects the base perpendicularly. (b) In any plane triangle the sum of the angles is 180°. (c) The exterior angle of a triangle is equal to the sum of the two opposite interior angles. (d) In a right triangle the square on the hypotenuse is equal to...

...are equal. COR. III. The acute angles of a right triangle are complements of each other. THEOREM 19. The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.^ ^ THEOREM 20. The sum of the interior angles of a polygon of...