...angles are unequal, and the greater angle is opposite the greater side.] PROPOSITION XXII. THEOREM 70. If two triangles have two sides and the included angle...the included angle of the other, the triangles are equal. GIVEN—AB, AC, and a, of the triangle ABC respectively equal to A'B', A'C, and a', of the triangle...

...contradict the hypothesis that angle «>angle c. Therefore AB<BC. QED PROPOSITION XXII. THEOREM 70. If two triangles have two sides and the included angle...the included angle of the other, the triangles are equal. C' GIVEN — AB, AC, and a, of the triangle ABC respectively equal to A'B', A'C, and a', of...

...equal, the figure is a rectangle. 46. Prove by coincidence that two parallelograms are equal if they have two sides and the included angle of one equal respectively to two sides and the included angle of the other. 42 PLANE GEOMETRY PROPOSITION XXVIII 109. Theorem. // two sides of a quadrilateral are...

...on a fixed great circle. 26. If two spherical triangles have two sides and the included angle of the one equal respectively to two sides and the included angle of the other, the two triangles are equal or symmetrical. 27. If two convex spherical triangles have two sides of the...

...contradict the hypothesis that angle «> angle c. Therefore AB>BC QED PROPOSITION XXII. THEOREM 78. If two triangles have two sides and the included angle...and the included angle of the other, the triangles arc equal. JB' C' GIVEN — AB, AC, and a, of the triangle ABC respectively equal to A'B', A'C, and...

...PROBLEM. To construct a square on a given side. PROPOSITION XXVI. THEOREM. 115. If two parallelograms have two sides and the included angle of one equal...two sides and the included angle of the other, the parallelograms are equal. 7 ».D *a FIG. 53. [Superpose, and use Ax. III.] 116. COR. If two rectangles...

...contradict the hypothesis that angle «>angle c. Therefore AB<BC. QED PROPOSITION XXII. THEOREM 70. If two triangles have two sides and the included angle...equal respectively to two sides and the included angle of the othcr, the triangles are equal. C' GIVEN — AB, AC, and a, of the triangle ABC respectively...

...triangle /iCJSf= triangle AC'X. §78 [If two triangles have two sides, and the included angle of the one equal respectively to two sides and the included angle of the other, the triangles are equal.] Hence XC=XC'. Now BC'<BX+XC'. §7 [A straight line is the shortest path between any two of...

...I. (MODEL FOR PUPILS.) /. Theorem. If any two triangles have two sides and the included angle of the one equal respectively to two sides and the included angle of the other, the triangles are equal. //. Given: Д ABC and Л DEF, in which (1) AB = DE, (2) A С = D К, and (3) z BA С = ZED F....

...§ 600.) PROP. XXII. THEOREM. 602. If two spherical triangles on the same sphere, or equal spheres, have two sides and the included angle of one equal,...respectively, to two sides and the included angle of the other, II. They are symmetrical if the equal parts occur in the reverse order. I. Given ABC...