...demonstration is that which is given to the XXVI of Euclid, though usually stated in a different way, namely : "If two sides and the included angle of one triangle...respectively to two sides and the included angle of another triangle the two triangles are equal," &c. In this case the demonstration is purely geometrical, and...

...triangles are equal throughout. T. Put that into a single statement. Teacher obtains from P. : When two sides and the included angle of one triangle are equal respectively to two sides, etc. T. We can show that this must be true always, as follows. The general proof of the proposition...

...Analysis. 1°. because e — e'. d is J_ c because & = V. 2°. b = b' Proof, e = e' because c = c' (if two sides and the included angle of one triangle are equal, etc.) . -. b = V, § 18. But if b = b' and c = c', then d is J_ to 'c. (If a straight line have two...

...conclusion. Thus in Proposition I. we have: Hypothesis.—If two sides and the included angle of any triangle are equal, respectively, to two sides and the included angle of another triangle, conclusion, the triangles are equal. II. The Particular Enunciation, which refers to the...

...If the equality of certain parts is known, the equality of the other parts can be established — eg if two sides and the included angle of one triangle are equal to the corresponding parts of another, the triangles are congruent, since the remaining parts are also...

...them as to size? Are they equal? Why? From Problem B we learn that : Two triangles are equal when 2 sides and the included angle of one triangle are equal, respectively, to 2 sides and the included angle of the other. Draw two triangles as ABC and DEF with two sides and the...

...If the equality of certain parts is known, the equality of the other parts can be established — eg if two sides and the included angle of one triangle are equal to the corresponding parts of another, the triangles are congruent, since the remaining parts are also...

...triangles are congruent. 292. We have thus far proved three theorems on congruent triangles, viz. : I. If two sides and the included angle of one triangle are equal, each to each, to two sides and the included angle of another triangle, the triangles are congruent....

...4. What relation as to form and size do the whole triangles ABC and CDE seem to have ? 145. THEOREM: If two sides and the included angle of one triangle are equal, each to each, to two sides and the included angle of another triangle, the triangles are equal in all...

...congruency is ^. Thus, ABC = A'B'C' means ABC and A'B'C' may be made to coincide. PROPOSITION I 24. Theorem: If two sides and the included angle of one triangle...respectively, to two sides and the included angle of another triangle, the triangles are congruent. c ,, FIG. 14 Conclusion: Then the triangles ABC and A'B'C' are...