 | University of St. Andrews - 1903 - 764 pages
...consecutive rays are given. 4. Define reciprocally proportional, and prove thai parallelograms which have an angle of the one equal to an angle of the other and their sides about the equal angles reciprocally proportional are equal in area. TP and TQ are tangents... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...the polygon. D 190 AREAS OF POLYGONS. PROPOSITION VII. THEOREM. 410. The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. Let the triangles ABC and... | |
 | Cora Lenore Williams - Geometry - 1905 - 56 pages
...the lines, the ratio of similitude. Prop. 110. Mutually equiangular triangles are similar. Prop. 111. If two triangles have an angle of the one equal to an angle of the other, and the including sides proportional, they are similar. Prop. 112. If two triangles have their corresponding... | |
 | Education - 1879 - 928 pages
...they have two angles of the one equal to two angles of the other; Two triangles are similar If they have an angle of the one equal to an angle of the other and the including sides proportional ; Two triangles are similar If they have their sides respectively proportional."... | |
 | Education - 1907 - 880 pages
...have two angles of the one equal to two angles of the other; Two triangles are similar if they have nn angle of the one equal to an angle of the other and the including sides proportional ; Two triangles are similar if they have their sides respectively proportional."... | |
 | Cora Lenore Williams - Geometry - 1905 - 122 pages
...parallelograms have two adjacent sides of the one equal respectively to two adjacent sides of the other, and an angle of the one equal to an angle of the other, the parallelograms are congruent. Prop. 78. Two rectangles are congruent if two adjacent sides of the... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...is a mean proportional between the segments of the other. 51. Two parallelograms are similar if they have an angle of the one equal to an angle of the other and the including sides proportional. 52. Two rectangles are similar if two adjoining pairs of homologous sides... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 pages
...trapezoids are then computed by the previous theorems. PROPOSITION VII. THEOREM 414 Two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. HYPOTHESIS. The & ABC and... | |
 | 1906 - 818 pages
...which touches it. 2. To describe a circle about a given regular pentagon. 3. Equal triangles which have an angle of the one equal to an angle of the other have their sides about those angles reciprocally proportional ; and triangles which have an angle of... | |
 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...trapezoids are then computed by the previous theorems. 198 PROPOSITION VII. THEOREM 414 Two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. HYPOTHESIS. The & ABC and... | |
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The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C'... 
