...face angle of a polyedral angle is less than the siun of all the others. PROPOSITION XIV. THEOREM 784. Two triangles on the same sphere are equal: I. If...arranged in the same order in both triangles. Proof — I, II. The proof for the corresponding propositions in Plane Geometry will apply. §§ 78, 81 III....

...Hint.—Divide the polygon into triangles by diagonals from any vertex. PROPOSITION XIV. THEOREM 784. Two triangles on the same sphere are equal: I. If...are arranged in the same order in both triangles. Proof—I, II. The proof for the corresponding propositions in Plane Geometry will apply. §§ 78,...

...conclusions are contrary to the hypothesis. Therefore ABC>ACB. QED 389 PROPOSITION XXVI. THEOREM 87 3. Two triangles on the same sphere are equal : I. If...corresponding triedral angles are equal. §§ 595. 596- 597 . ED PROPOSITION XXVII. THEOREM 874. Two triangles on the same sphere are symmetrical : I. If two sides...

...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 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...

...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....

...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,...

...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) 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,...