...invention, and judgment." Instead of a series of written proofs to memorize, such as, for instance, the sum of the three angles of a triangle is equal to two right angles, the student takes the triangle, and, with suggestions from the teacher where necessary, works...

...circular bed and the area of the hexagonal bed. Yale, June, J896. GEOMETRY (A). TIME, ONE HOUR. 1. The sum of the three angles of a triangle is equal to two right angles. 2. Construct a circle having its center in a given line and passing through two given points. 3. The bisector...

...logarithms.) Princeton, June, Í896. State what text-book you have read and how much of it. 1. Prove that the sum of the three angles of a triangle is equal to two right angles; and that the sum of all the interior angles of a polygon ofя sides is equal to (n — 2) times...

...circular sheet of tin 16 inches in diameter and weighing 8.2 ounces per square foot. JUNE 1896. (a) 1. The sum of the three angles of a triangle is equal to two right angles. 2. Construct a circle having its center in a given line and passing through two given points. 3. The bisector...

...axioms, and, in short, came to make perfect demonstrations. In this way he arrived unaided at the theorem that the sum of the three angles of a triangle is equal to two right angles. His father caught him in the act of studying this theorem, and was so astonished at the sublimity...

...circular sheet of tin 16 inches in diameter and weighing 8.2 ounces per square foot. JUNE 1896. (a) 1. The sum of the three angles of a triangle is equal to two right angles. 2. Construct a circle having its center in a given line and passing through two given points. 3. The bisector...

...a triangle is greater than the difference of the other two sides. PROPOSITION XII. THEOREM. 79. The sum of the three angles of a triangle is equal to two right angles. Let ABC be any triangle. To prove that Z A + Z B + Z BC A is equal to two right angles. From...

...180° ; . : the required ¿. = 180° - 76° = 104°. Ex. 59. Show by each of the following figures that the sum of the three angles of a triangle is equal to two right angles, assuming that the construction lines чrе drawn as they appear to be drawn. Proof. (1) §...

...opposite angles of an inscribed quadrilateral are supplementary. Ex. 283. Prove by the use of Prop. 124 that the sum of the three angles of a triangle is equal to two right angles. Proposition 125. Problem. 158. At a given point in a given straight line, to erect a perpendicular...

...sides opposite the equal angles are called homologous sides. PROPOSITION XVIII. THEOREM. 129. Tlie sum of the three angles of a triangle is equal to two right angles. BE A c ~F Let A, B, and BCA be the angles of the triangle ABC. To prove that ZA + ZB + Z BCA...