...in a triangle 6. If they are the opposite angles of a parallelogram III. Two triangles are equal: 1. If two sides and the included angle of one are equal respectively to two sides and the included angle of the other 2. If two angles and the included side are equal respectively to two angles and the included...

...about the properties of space is built up, such, for instance, as the fact 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 ; and upon these facts are based nearly all indirect measurements. Without geometry it...

...about the properties of space is built up, such, for instance, as the fact 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 ; and upon these facts are based nearly all indirect measurements. Without geometry it...

...parallelogram is the center of symmetry of the parallelogram. CONGRUENCE OF PARALLELOGRAMS 98. THEOREM 35. Two parallelograms are congruent if two sides and the included angle of one are equal to two sides and the included angle of the other. FIG. 152 Hypothesis: In S] ABCD and A'B'C'D', w =...

...coinciding with AA'B'C'1? Are the triangles congruent? Complete the following statement : Two triangles are congruent if two sides and the included angle of one are equal respectively to • • • . THEOREM. Two SIDES AND INCLUDED ANGLE 58. Tivo triangles are congruent if two sides and...

...SYMMETRICAL 329. THEOREM XII. Two triangles on the same sphere, or on equal spheres, are equal or symmetrical if two sides and the included angle of one are equal respectively to two sides and the included angle of the other. Proof : This is a direct corollary of the theorems §§ 142, 150. 330. Vertical Spherical...

...SYMMETRICAL 329. THEOREM XII. Two triangles on the same sphere, or on equal spheres, are equal or symmetrical if two sides and the included angle of one are equal respectively to two sides and the included angle of the other. Proof : This is a direct corollary of the theorems §§ 142, 150. 330. Vertical Spherical...

...Theorem PROPOSITION I CONGRUENCE OF TRIANGLES Theorem: Two SIDES AND THE INCLUDED ANGLE. Two triangles are congruent if two sides and the included angle...equal respectively to two sides and the included angle of the other. CZ Given the triangles ABC and XYZ, with AB equal to XY, AC equal to XZ, and angle A...

...adjacent angles of a parallelogram intersect each other at right angles. 79. Two parallelograms are equal if two sides and the included angle of one are equal respectively to two sides and the included angle of the other. 80. The image of an object A seen in a ., plane mirror by the eye at K appears to be...

...of the first. For example, the converse of Theorem 1 is as follows : If two triangles are congruent, two sides and the included angle of one are equal respectively to two sides and the included angle of the other. EXERCISES 18. State the hypotheses of Theorems 1 to 10 inclusive. State the conclusions....