...sides opposite the equal angles are called homologous sides. PROPOSITION XVIII. THEOREM. 129. Tfie sum of the three angles of a triangle is equal to two right angles. Let A, B, and BCA be the angles of the triangle ABC. To prove that ZA + ZB + Z BCA = 2 rt....

...pentagon are 40.5, 30.6'>, 51.25, 32.75, and 36.85; find the perimeter. Ans. 192 ft. TRIANGLES. 47. The sum of the three angles of a triangle is equal to two right angles, <>r 180°. Thus, the sum of the three angles A, B, and C, Fig. 31, is 59° + 73° + 48° =...

...equals the sum of Zs CAB and CBA That is, Z.ACD equals the sum of Zs CAB and CBA. 101. COROLLARY I. The sum of the three angles of a triangle is equal to two right angles. 102. COROLLARY II. The two acute angles of any right triangle are complementary ; ie their...

...such statements and demand no more demonstration than if a man remarked it was a warm day! Apropos of the proposition that the sum of the three angles of a triangle equals two right angles, our Socrates has a jeu d esprit that is positively cute. Quoth he : "A triangle...

...the place of mathematical demonstration. No experimental process can ever establish the general truth that the sum of the three angles of a triangle is equal to two right angles. We should not confound " geometrical recreations'" with geometrical science.—(P.) t Isoperimetric...

...incidentally, its angle increases uniformly. Casey (El. of Euclid, 8th ed., p. 299) says : " The discovery of the proposition that ' the sum of the three angles of a triangle is equal to two right angles ' is attributed to Pythagoras. Until modern times no proof of it, independent of the theory...

...Isosceles. 1 f Acute. -{ I Oblique. Scalene. f Isosceles. v. Obtuse. 82 PROPOSITION XI. THEOREM 153 The sum of the three angles of a triangle is equal to two right angles.* HYPOTHESIS. ABC is any triangle. CONCLUSION. ZA + ZB + ZC = 2rt. A. PROOF Draw MN through...

...Scalene. f Isosceles. fc Oblique. Acute. Scalene. f Isosceles. . Obtuse. PROPOSITION XL THEOREM 153 The sum of the three angles of a triangle is equal to two right angles.* HYPOTHESIS. ABC is any triangle. CONCLUSION. PROOF Draw MN through B II to AC, and produce...

...to the bearing of these propositions upon Euclid's Postulate 5 ; and the next theorem is VII. If the sum of the three angles of a triangle is equal to two right angles, through any point in a plane there can only be drawn one parallel to a given straight line....

...body of scientific theorems. Allman attributes to Thales the discovery of the two theorems — (a) The sum of the three angles of a triangle is equal to two right angles ; (&) The sides of equi-angular triangles are proportional. (Hence the basis of the theory of...