...F respectively. Prove that, if DE=EF, BD = CF. Ex. 867. If two triangles have two sides of the one equal to two sides of the other, each to each, and the angles opposite to two equal sides equal, the angles opposite the other equal sides are either equal...

...(b.) Prove the correctness of your construction. (10) 8. If two triangles have two sides of the one equal to two sides of the other each to each, and the angles included by those sides equal, show that the triangles are equal in all respects. 0 is the centre...

...the other sides are equal, the triangle is isosceles. 2. If two triangles have two sides of the one equal to two sides of the other, each to each, and the included angles unequal, the triangle which has the greater included angle nas the greater third side. 3. Find the...

...angles are opposite to equal sides. THEOREM 4. [Euclid I. 4.] If two triangles have two sides of the one equal to two sides of the other, each to each, and the angles include^ by those sides equal, then the triangles are equal in all respecf" Let ABC, DEF be...

...between two given parallels may be of a given length. 6. If two triangles have two sides of the one equal to two sides of the other, each to each, and the angles included by those sides equal, then the triangles are equal in all respects. 7. If one side...

...Two triangles are congruent (ie are equal in every respect) if they have — (a) two sidea of the one equal to two sides of the other, each to each, and the angle contained by the two sides of the one equal to the angle contained by the two corresponding sides...

...whose sides are 2 in. and 1 in. and one of whose angles is 60°. Ex. 7. Construct two triangles which have two sides of one triangle equal to two sides of the other, and the angles opposite one pair of corresponding sides equal, but having the equal parts so arranged...

...so is seen when the triangles OXll' and OPR are compared. These triangles have two sides of the one equal to two sides of the other, each to each, and the angle at 0 between them common to both. Hence the angle OR'X is equal to the angle ORP which is a right...

...of the Ambiguous Case are noteworthy : — Converse (1) If two triangles have two sides of the one equal to two sides of the other, each to each, and the angles opposite to one pair of equal sides supplementary, then the angles opposite to the other pair...

...think deserves to be interpolated. Th. 20 (p. 34) is new. ' If two Triangles have two sides of the one equal to two sides of the other, each to each, and the angles opposite to tivo equal sides equal, the angles opposite to the other two equal sides are either...