...equal angles being homologous, the third angles of the triangles are either equal or supplementary. The internal bisector of an angle of a triangle divides...of the sides containing the angle, and likewise the «eternal bisector externally. In a right-angled triangle the perpendicular drawn from the right angle...

...equal angles being homologous, the third angles of the triangles aro either equal or supplementary. The internal bisector of an angle of a triangle divides...in the ratio of the sides containing the angle, and likewiee the external bisector externally. In a right-angled triangle the perpendicular drawn from...

...QR=p, RP = g, PQ = r. Also, AABC ~ APQR. ~, abca + b + c To prove : —=—=-= . PQ r p+q+r Theorem 4. The internal bisector of an angle of a triangle divides...internally in the ratio of the sides containing the angle. Given : A AABC in which AD, the bisector of ZA, meets BC in D. BD AB Toprove:— = —. Theorem 5....

...touch two given straight lines and pass through a given point. THIRD STAGE. BOOK IV THEOREM 8 (i). The internal bisector of an angle of a triangle divides...internally in the ratio of the sides containing the angle. fig. 264. Dala ABC is a triangle, AD bisects L BAC internally and cuts BC at D. To prove tJtat —...

...Theorems Th. 49 enables us to prove the following interesting results about a triangle. THEOREM 56 (i). The internal bisector of an angle of a triangle divides...internally in the ratio of the sides containing the angle. THEOREM 56 (ii). The external bisector of an angle of a triangle divides the opposite side externally...

...on corresponding sides . . . .118 NOTE ON THE RATIO OP AREAS OP TRIANGLES .... 118 THEOREM 58 (i). The internal bisector of an angle of a triangle divides...internally in the ratio of the sides containing the angle ........ 118 THEOREM 58 (ii). The external bisector of an angle of a triangle divides the opposite...

...through the point of contact, show that the chords joining their extremities are parallel. 9. Prove that the internal bisector of an angle of a triangle divides...internally in the ratio of the sides containing the angle. In a triangle ABC, D is the middle point of the side BC. DE and DF are drawn bisecting angles ADB,...

...Calculate AB : AC and the ratio in which D divides the base BC (see p. 304). BOOK IV THEOREM 8 (i). The internal bisector of an angle of a triangle divides...internally in the ratio of the sides containing the angle. u DC fig. 323. Data ABC is a triangle, AD bisects L. BAC internally and cuts BC at D. DB AB To prove...

...triangles are similar . . . ... 38 Xote on theorems on similarity vf triangles .... . . .38 THEOREM 30 (i). The internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the side* containing the .angle •. 3t) AREA. PARE THEOREM 31. Parallelograms on the same base and between...

...supplementary. The internal bisector of an angle of a triangle divides the opposite sideinternally in the ratio of the sides containing the angle, and likewise the external bisector externally. In a right-angled triangle the perpendicular drawn from the right angleto the base will divide the...