...Prove that the area of a circle of which r is the radius is equal to if t 2 . VII. 1. Prove that if two triangles have two sides of the one respectively equal to two sides of the other, while the included angles are unequal, the third sides will be unequal, and the greater third side...

...then the angle of one triangle is supplemental to the other. Hence the following property : — If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal. A distinction ought to be made between...

...B = E (53, 5), and the triangles are equal, as just shown. 73. Proposition XXIX.— Theorem. If two triangles have two sides of the one respectively equal to two sides of the other, and the included angle of the one greater than the included angle of the other, the third side of the one having...

...a similar set. It may, for instance, be used to prove the converse of (6), namely : — " When two triangles have two sides of the one respectively equal to two sides of the other, but the base of one greater than the base of the other, the vertical angle which is opposite the greater...

...secured by bringing together the two greatest sides. PROPOSITION X. Fio. 210. 295. Theorem.—If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the third sides are unequal, and the greater third side belongs to the triangle...

...GEOMETRY. 1. DEFINE a plane, a parallelogram, a trapezoid, a tangent to a circle. 2. Prove that when two triangles have two sides of the one respectively equal to two sides of the other and the included angle of the first greater than the included angle of the second, the third side of the first...

...angle. CoR 19 25. Given the three bisectors of the sides of a triangle ; construct it. DBF 20 26. If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, they are equal in area 20 27. If squares be described on the sides of...

...Ans.—£2112. GEOMETRY. Examiners—Prof. AG GREENHILL, MA, and BENJAMIN WILLIAMSON, Esq., MA, FRS 1. If two triangles have two sides of the one respectively equal to two sides of the other, but the contained angle of the one greater than the contained angle of the other, prove that the base...

...the equal angles lie opposite the equal sides. ELEMENTS OF PLANE GEOMETRY. THEOREM XXVII. 89. If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the third sides are unequal, and the greater third side is in the triangle...

...triangles, the equal angles lie opposite the equal sides. PROPOSITION VIII. 307. Theorem.— If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the third sides are unequal, and the greater third side belongs to the triangle...