...Euclid may be assumed. Mr. EARDLEY, Head Inspector. Mr. PEDLOW, District Inspector. 1. Prove that if two triangles have two sides of the one equal respectively to two sides of the other, but their buses unequal, their vertical angles are unequal (10 marks) ; and show that if the diagonals...

...coincide throughout, and are equal. % PROP. XXVIII. THEOREM. 91. If two triangles have two sides of one equal respectively to two 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...

...the area of a segment whose arc is 60°. SEPTEMBER 1901. PLANE. 1. If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than...

...alternate interior angles equal, the two lines are parallel. 2. If two triangles have two sides of one equal respectively to two 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...

...parts are equal.] (§ 66) Again, if we suppose Z A < Z D, BC would be < EF. [If two & have two sides of one equal respectively to two sides of the other, but the included Z of the first > the included Z of the second, the third side of the first is > the third side of the...

...included by a side and the base produced. BOOK I. PLANE GEOMETRY. PROPOSITION XXVIII. THEOREM. 154. If two triangles have two sides of the one equal, respectively,...sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater...

...angle included by a side and the base produced. PROPOSITION XXVIII. THEOREM. 154. If two triangles hace two sides of 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 the third side of the first is greater...

...= 60°. .'. &ACD is equilateral (why ?), and AD, half of AB = AC. .'.AB-2AC. ' •B Ex. 23. If two triangles have two sides of the one equal, respectively, to two sides of the other, and the angles opposite two equal sides equal, the angles opposite the other two equal sides are equal...

...Zc = 60°. .'. &ACD is equilateral (why ?), and AD, half of AB = AC. .-.AB = 2AC. " K Ex. 23. If two triangles have two sides of the one equal, respectively, to two sides of the other, and the angles opposite two equal sides equal, the angles opposite the other two equal sides are equal...

...the vertex, is parallel to the base. Proposition 49. Theorem. 60. If two triangles have two sides of one equal respectively to two 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...