Plane Geometry Developed by the Syllabus Method

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1909 edition. Excerpt: ... SECTION VIII. TRIANGLE THEOREMS 92. Theorem I. If two triangles have two sides and the included angle of the one respectively equal to two sides and the included angle of the other, the triangles are congruent. Analysis Class. Triangles congruent. Known Methods. Coincidence, using the axiom of motion. Method to be used. One triangle will be supposed to be placed on the other, and the given facts will then be used to determine whether they would coincide. II. B-would fall on E, - nc = Ef (given). A would fall on D, -.- CA = FD (given). III. AB would coincide with DE (but one straight line through two points). IV. .-. A ABC si A DEF (def. =s). Note. It often makes the conditions of the theorem more clear if those conditions are indicated in the figure. The usual way of showing equal parts is to place a like mark on any two parts that are known to be equal. In the figure used in Th. I, the equal parts are indicated by such marks. Where equal parts are used in the theorem, although not given, the same method is sometimes used. 93. Corresponding Parts of Congruent Figures. When two figures coincide, each part (side or angle) of one coincides with a part of the other, and is therefore equal to it. Two parts of congruent figures that would coincide if the figures were made to coincide are called corresponding, or homologous parts. When two figures are known to be congruent on account of their having certain equal parts, -- as by Th. I, -- the other corresponding parts can be told by their position relative to the known parts; as, by their being opposite to known parts, or between two known parts. In Th. I, AB -- DE, Z A = Z . D, Z B = Z E. The most important use of congruence of figures is to prove equality of lines and of angles. 94. Theorem...