...invariable. Under what conditions will this difference be /ею :' 2. Equal triangles on the same base, and on the same side of it, are between the same parallels. The sides .11! and .K'of a triangle are bisected in I) and E respectively, and RE, CD are produced...

...CONCLUSION. AB + AC<A'B + AC. PROOF. AA || BC. (253. INVERSE. Equivalent triangles on the same base, and on the same side of it, are between the same parallels.) Draw CND _L AA \ meeting BA produced in D. Join A'D. 4NAC = 4ACB, (168. If a transversal cuts two parallels,...

...equal to half the trapezium. PEOP. XXXIX.— THEOREM. Equal triangles (BAC, BDC) on the same bose (BC) and on the same side of it are between the same parallels. Dem. — Join AD. Then if AD be not parallel to BC, let AE be parallel to it, and let it cut BD in...

...parallelograms about the diameter of a square are likewise squares. 5. Equal triangles on the same base, and on the same side of it, are between the same parallels. 6. If a straight line be bisected, and produced to any point, the square on the whole line thus produced,...

...are equal to twice as many right angles as the figure has sides. 3. Equal triangles on the same base, and on the same side of it, are between the same parallels. If two equal lines AB, CD cross one another, and А С is equal to BD, then shall AD be parallel to...

...CONCLUSION. AB + AC < A'B + A'C. PROOF. A A' || BC. (253. INVERSE. Equivalent triangles on the same base, and on the same side of it, are between the same parallels.) Draw CND ± A A', meeting BA produced in D. Join A'D. 4NAC = £ACB, (168. If a transversal cuts two...

...point draw a right line parallel to a given right line. 4. Prove that equal triangles on the same base and on the same side of it are between the same parallels. 5. The sum of the four angles of any quadrilateral is equal to four right angles. 6. Prove that the...

...to a given rectilineal figure. (Syllabus.) PROPOSITION 39. THEOREM. Equal triangles on the same base and on the same side of it are between the same parallels. Let ABC and DBC be equal As on the same base BC, and on the same side of it, they shall be between...

.../. A ABP = A CDQ. Proposition 39. THEOREM — Triangles of equal area, which are on the same base, and on the same side of it, are between the same parallels. Let AS PAB, QAB be equal in area, and on the same side of same base AB. Assume that the || to AB, through...

...of it are between the same parallels. 40. Equal triangles on equal bases in the same straight line and on the same side of it are between the same parallels. 41. If a parallelogram and a triangle be on the same base and between the same parallels, the parallelogram...