...triangles. Proof. — In each case the corresponding triedral angles are equal. §§ 595. 596, 597 PROPOSITION XXVII. THEOREM 874. Two triangles on the...triangles are symmetrical. § 851 QED POLAR TRIANGLES 873. Def. — If, with the vertices of a spherical triangle as poles, arcs of great circles are described,...

...and BOC, how many degrees are there in. jiDOEt PBOP. XVII. THEOREM. 69. Two triangles are equal when the three sides of one are equal respectively to the three sides of the other. CF 1) Given, in A ABC and DEF, AB = DE, BC=EF, and CA = FD. To Prove A ABC = A DEF. Proof. Place A...

...point in the _L is equally distant from the extremities of the line.] (§ 41, I) [Two A are equal when the three sides of one are equal respectively to the three sides of the other.] (§ 69) Now revolve A BCD about CD as an axis until it coincides with A B'CD. Then, point B will fall...

...and include an angle bisected by that line. Proposition 2O. Theorem. 30. Two triangles are equal when the three sides of one are equal respectively to the three sides of the other. Hypothesis. In the A ABC and DEF, AB = DE, AC = DF, and BC = EF. Conclusion. A ABC = A DEF. Proof....

...And since AC and AD are _L to BB' at its middle point, BC = B'C and BD = B'D. [Two & are equal when the three sides of one are equal respectively to the three sides of the other.] (§ 69) Now revolve A BCD about CD as an axis until it coincides with A B'CD. Then, point B will fall...

...methods. 1917 MATHEMATICS C— PLANE GEOMETRY Monday 2 pm Two hours 1. Prove: Two triangles are congruent if the three sides of one are equal, respectively, to the three sides of the other. 2. a) Prove: If two chords intersect within a circle, the product of the segments of one is equal to...

...included angle of one are equal, respectively, to two sides and the included angle of the other. (3) If the three sides of one are equal, respectively, to the three sides of the other. (4) If the triangles are right triangles and have a leg and the hypotenuse of one equal, respectively,...

...included angle of one are equal, respectively, to two sides and the included angle of the other. (3) lf the three sides of one are equal, respectively, to the three sides of the other. (4) If the triangles are right triangles and have a leg and the hypotenuse of one equal, respectively,...

...BC. Hence AB = BC. m QEB BOOK I. PLANE GEOMETRY PROPOSITION XI. THEOREM 101. Two triangles are equal if the three sides of one are equal, respectively, to the three sides of the other. B Given the A ABC and DEF in which AB EF, au&AG=DF. To prove A ABC= A DEF. Proof. Place the & ABC so...

...AB is not less than BC. Hence AB=BC. 0. EB PROPOSITION XI. THEOREM -* 101. Two triangles are equal if the three sides of one are equal, respectively, to the three sides of the other. BE J B Given the A ABC and DEF in which AB = DE, EF, and AC=DF. To prove AABC=ADEF. Proof. Place the...