...triangles and trapezoids are then computed by the previous theorems. 198 PROPOSITION VII. THEOREM 414 Two triangles which have an angle of the one equal...products of the sides including the equal angles. HYPOTHESIS. The & ABC and ADE have the ZA common. A ABC AB x AC CONCLUSION. A ADE AD x AE PROOF Draw...

...(Necessary to prove propositions concerning concurrent lines.) *P16. Triangles that have an angle of one equal to an angle of the other, are to each other as the products of the sides containing those angles. *P18. In any obtuse triangle, the square of the side opposite the obtuse angle...

...GEO.METRY 388. THEOREM. If two triangles have an angle of one equal to an angle of the other, they are to each other as the products of the sides including the equal angles. Given: A ABC and DEF, ZA = Z D. To Prove : A ABC _ AB -AC A DEF ~ DE - DF Proof : Superpose A ABC upon...

...THEOREM 675 The volumes of two tetraedrons, having a triedral angle of the one equal to a triedral angle of the other, are to each other as the products of the three edges of the equal triedral angles. HYPOTHESIS. V and V are the volumes of the two tetraedrons...

...is measured by one-half the difference of the intersected arcs. 3. Two triangles, having an angle of one equal to an angle of the other, are to each other as the product of the sides including the equal angles. Prove. 4. If the radius of a circle is 3v% what is...

...THEOREM. Two triangular pyramids (tetrahedrons) having a trihedral angle of one equal to a trihedral angle of the other are to each other as the products of the three edges including the equal trihedral angles. Given : Triangular pyramids S-ABC, S—PQR; having...

...the trapezoid change ? Draw the trapezoid. PROP. VIII. THEOREM 290. Two triangles having an angle of one equal to an angle of the other, are to each other as the products of tlw sides including the equal angles. A a' Draw A AB'C' and line BC meeting AB' at B, and AC' at...

...trapezoid change ? Draw the trapezoid. , PROP. VIII. THEOREM 290. Two triangles having an angle of one equal to an angle of the other, are to each other as the products of tlw sides including the equal angles. A Draw A AB'C' and line BC meeting AB' at B, and AC' at C....

...through a point in the circumference of a circle two chords are drawn, 4. (a) Two triangles having an angle of the one equal to an angle of the other...products of the sides including the equal angles. (b) To trisect a right angle. (c) Through a point to draw a line parallel to a given line. 5. The bisectors...

...less than, the opposite angle of the other, and conversely. (5) Areas of triangles having an angle of one equal to an angle of the other are to each other as the products of the including sides. B. PLANE GEOMETRY PROPOSITIONS THAT CAN BE USED IN SOLID GEOMETRY BECAUSE THE NATURE...