...in a circle whose radius is 11.529 inches. Cornell, 1894. 1. If two triangles have two sides of the one equal, respectively, to two sides of the other,...first is greater than the third side of the second. Prove this ; and state the converse. 2. Prove that lines drawn through the vertices of a triangle to...

...the one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then...first is greater than the third side of the second. 153. If two sides of a triangle are equal respectively to two sides of another, but the third side...

...problem is impossible if one of the given lines is equal to or greater than the sum of the other two. 91. Exercise. — By Proposition XXIV. prove that each...second. GIVEN— two triangles ABC and A'B'C having Aff=A'B' and AC— AC', but angle ^4>angle A. To PROVE BC>B'C. Apply A'B'C to ABC making A'B' coincide...

...having two sides and the included angle respectively equal are equal.] If A <A' then would BC<B'C. § 91 [If two triangles have two sides of one equal respectively...first is greater than the third side of the second.] But both these conclusions contradict the hypothesis. Therefore A> A' '. QED 03. CONSTRUCTION. To construct...

...THEOREM. 78. If two trianyles have two sides of one equal respectively to two sides of the oiJier, but the included angle of the first greater than the...first is greater than the third side of the second. Let the triangles ABC and XYZ have AB = XY, AC = XZ, angle BA C greater than angle X. It is to be proved...

...sides of the other but the included angle of the first greater than the included angle of the second, the third side of the first is greater than the third side of the second. 3. Demonstrate: The line joining the vertex of the right angle of a right triangle to the center of...

...radius of a circle is 10 iuches; find the area of a segment whose arc is 60°. SEPTEMBER 1901. PLANE. 1. If two triangles have two sides of one equal respectively...first is greater than the third side of the second. State and prove the converse theorem. 2. To divide a given straight line into segments proportional...

...sides of the other, but the included angle ot the first greater than the included angle of the second, the third side of the first is greater than the third side of the second. 3. The diagonals of a rhombus bisect each other at right angles. 4. In the same circle or equal circles,...

...sides of the other, but the included angle of the first greater than the included angle of the second, the third side of the first is greater than the third side of the second. JB* A tf Given, in A ABC and DEF, AB = DE, AC= DF, and Z BAC > Z D. To Prove BC>EF. Proof. Place A...

...the included angle of the first greater than the included angle of the second, then the a Y> Fio. 46. third side of the first is greater than the third side of the Let the triangles ABC and XYZ have AB = XY, AC = XZ, angle BA C greater than angle A*. It is to be...