| 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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