...7. State the conditions under which two triangles are congruent. Two triangles are congruent : (i) If two sides and the included angle of the one are...equal respectively to two sides and the included angle of the other. (ii) If two angles and the included side of the one are equal respectively to two angles...

...points. •'• A ABC = A A'B'C' for they can be made to coincide. Therefore, Two triangles are congruent if two sides and the included angle of the one are...equal respectively to two sides and the included angle of the other. 1. To find the distance across an impassable marsh: Stake off two lines AC and I1D that...

...all. And he will be able without reading the proof in the text, to apply this method in proving that "Two triangles are equal if two sides and the included angle of one are equal respectively to two sides and the included angle of the other," or that "Two triangles...

...adjacent angles of one are equal respectively to a side and the two adjacent angles of the other. 107. Two triangles are equal if two sides and the included angle of one are equal respectively to two sides and the included angle of the other. 110. Homologous parts...

...easily carried out it is left to the student.] 88. Theorem XXIII. Two parallelograms are congruent if two sides and the included angle of the one are...equal respectively to two sides and the included angle of the other. B' Fro. 59 Given the O ABCD and A'B'C'D' in which AB = A'B', AD = A'D', and Z DAB = Z...

...Corresponding parts of congruent figuv are equal. PROPOSITION II. THEOREM 68. Two triangles are congruent if two sides and the included angle of the one are...equal respectively to two sides and the included angle of the other. AB x Y Given the triangles ABC and XYZ, with AB equal to .XT, AC equal to XZ, and the...

...easily carried out it is left to the student.] 88. Theorem XXIII. Two parallelograms are congruent if two sides and the included angle of the one are...equal respectively to two sides and the included angle of the other. FIG. 59 Given the El ABC D and A'B'C'D' in which AB = A'B\ = A'D', and Z DAB= Z D'A'B'....

...diagonals of a parallelogram bisect each other. 88. Theorem XXIII. Two parallelograms are congruent if two sides and the included angle of the one are...respectively, to two sides and the included angle of the other. 89. Theorem XXIV. The line joining the middle points of the two sides of a triangle is...

...parts of congruent A are equal.) QED PROPOSITION XXX. THEOREM 132. Two parallelograms are congruent if two sides and the included angle of the one are equal respectively to hoo sides and the included angle of the other. c" AB A' B' Given the parallelograms ABCD and A'B'C'D',...

...equal.) .-. A ABC is congruent to A CDA. §68 (Two A are congruent if two sides and the included Z of the one are equal respectively to two sides and the included Z of the other.) .-.BC = AD, and ZA CB = Z CAD. § 67 .'. BC is II to AD. § 101 (When two lines in...