...right angles, (by the 13th.) .-. &c. •jy two triangles have two angles of the one respectively equal to two angles of the other, and a side of the one equal to a side of the other, whether it be adjacent or opposite to these equal angles, the remaining...

...have an immediate, and as it were intuitive, perception that it is less than the sum of the sides. ART. 46. " If two triangles have two angles of the...triangles are in every respect equal to each other." This theorem is of great use in Trigonometry; and in all measurements of surfaces, like ARTS. 3 and...

...equal, the triangle is isosceles. 2. If two triangles have two angles of the one respectively equal to two angles of the other, and a side of the one equal to a side of the other, either the sides adjacent to or opposite to those equal angles; the remaining...

...transposition. It might then be demonstrated as follows : If two triangles have two angles of the one equal to two angles of the other, and a side of the one equal to a corresponding side of the other; the triangles are equal in every respect. Given two triangles...

...have to one another the ratio of the sides of the triangle t .... 60 FIVE COROLLARIES 61 THEOREM 6. If two triangles have two angles of the one equal respectively to two angles of the other, the triangles shall be similar, the sides which are opposite the equal angles being homologous ............

...Fig. 28, therefore they are equal to each other. Fig. 27. Fig. 28. Because the triangles EAD and EBC have two angles of the one equal respectively to two angles of the other, therefore they are similar ; therefore _ - is equal to == ; xL,U Jiii therefore, the rectangle of AE...

...triangle are given, the third angle may be found by subtracting their sum from 180°. . 75. Corollary 2. If two triangles have two angles of the one equal respectively to two angles of the other, the third angles will also be equal. EXERCISES. 1. If a triangle has two angles each equal to 60°,...

...distances of the third angular point from the same two points. 2. If two triangles have two angles of one equal respectively to two angles of the other, and a side of one equal to a side similarly placed with respect to the equal angles of the other, the triangles are...

...the triangle which has the greater included angle has the greater base. 28. If two convex spherical triangles have two angles of the one equal respectively to two angles of the other, but the sides between these pairs of angles greater in one triangle than in the other, the triangle...

...is said to be the complement of another when the sum of the two is a right angle. 104. COROLLARY IV. If two triangles have two angles of the one equal respectively to two angles of the other, their third angles are also equal; or, if the sum of two angles in the one is equal to the sum of two...