...The exterior angle of a triangle is equal to the sum of the two opposite interior angles. 146. Cor. The exterior angle of a triangle is greater than either of the opposite interior angles. 147. Two triangles are equal if a side and two adjacent angles of the one...

...equilateral. (Why ?) s PROPOSITION V. 70. Theorem. If any side of a triangle is produced, the exterior angle is greater than either of the interior angles not adjacent to it. AB Given the A ABC, with AB produced to X. To prove that Z XBC > Z C, and also > Z BAC. Proof. 1. Suppose...

...each of the angles BAD and BCD, and that all the sides of the quadrilateral are equal. 4. Show that the exterior angle of a triangle is greater than either of the interior opposite angles. Hence show that every triangle must have at least two acute angles. 5. Prove that...

...two right angles, they cannot meet, even if produced indefinitely both ways. Corollary II. — Any exterior angle of a triangle is greater than either of the interior and opposite angles. Because any of the interior angles with its adjacent exterior angle equals two...

...produced.* SECTION 1. The Straight Line. Theor. G. If any side of a triangle is produced, the exterior angle is greater than either of the interior angles not adjacent to it. Prop. 31. Any two angles of a triangle are together less than two right angles. Prop. 32. If a triangle...

...angle. 2. Any exterior angle of a triangle equals the sum of the two non-adjacent interior angles. SCH. The exterior angle of a triangle is greater than either of the non-adjacent interior angles. a The exterior vertex angle of an isoangular triangle equals twice either...

...equals the sum of the other two opposite sides, a circle may be inscribed in the quadrilateral. An exterior angle of a triangle is greater than either of the interior angles not adjacent to it (taken up as the third theoiem). To divide a given line segment in mean and extreme ratio. SUGGESTION...

...within a triangle to the three vertices is less than the peri3 £ meter of the triangle. FIG- I(* 9. An exterior angle of a triangle is greater than either of the interior non-adjacent angles. Prove. 10. Prove angle D> angle A, Fig. 16. CHAPTER VIII THE OPERATIONS OF ARITHMETIC...

...are outside the circle. This follows from the proposition (also proved by means of the theorems that the exterior angle of a triangle is greater than either of the interior and opposite angles and that the greater angle is subtended by the greater side) which De Morgan proposes...

...L B+ Z ACB = Z ACD+ Z ACB. But Z ACD+ Z ACB = two rt. Zs, .-. Z A+ Z B+ Z ACB = two rt. Zs. Cor.— The exterior angle of a triangle is greater than either of the interior and opposite angles. 56.— Exercises ^1. Prove Theorem 10 by means of a st. line drawn through the...