...xx., Cor. i.) ; .-., e = fand а = dif. of _Ls. 4. The straight line joining the points of bisection of two sides of a triangle is parallel to the third side. Through one point of bisection draw a line | to the third side ; it will pass through the other point...

...1. The perpendicular is the shortest line which can be drawn from a point to a straight line. 2. The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to one-half of it. 3. Two parallel tangents intercept equal arcs on the circumference of...

...ED, GH, EG, and DH. Then since ED bisects AC and BC, it is parallel to AB, and equal to £ AB. [The line joining the middle points of two sides of a triangle is parallel to the third side, and equal to one-half of it.] (§ 130.) In like manner, since GH bisects OA and OB, it is parallel...

...one side of a triangle, parallel to a second side, bisects the third side. And, 2, the line through the middle points of two sides of a triangle is parallel to the third side. 85°. Theorem. — The three medians of a triangle pass through a common point. CF and AD are medians...

...parallel to AD and BC. II. To prove EF = \ (AD+BC). Since EG bisects AB and BD, EG = \AD. (1) [The line joining the middle points of two sides of a triangle is equal to one-half the third side.] (§ 130.) ' And since GF bisects BD and CD, GF= ^BC. (2) Adding...

...through the vertex, th. 27 or cor. 1 proves it. Draw the figure. 3. The line joining the mid-points of two sides of a triangle is parallel to the third side. For if not, suppose through the mid-point of one of those sides a line is drawn parallel to the base...

...through the vertex, th. 27 or cor. 1 proves it. Draw the figure. 3. The line joining the mid-points of two sides of a triangle is parallel to the third side. For if not, suppose through the mid-point of one of those sides a line is drawn parallel to the base...

...Two angles whose sides are perpendicular, each to each, are either equal or supplementary. (2) The line joining the middle points of two sides of a triangle is parallel to the third side, and equal to one-half of it. (3) The angle between a tangent and a chord is measured by one-half its...

...of any polygon is equal to four right angles. 44 PLANE GEOMETRY PROPOSITION XXXI 113. Theorem. The line joining the middle points of two sides of a triangle is parallel to the third side and equal to one-half of it. Appl. Cons. Dem. I = 1 II = II Prove DE II AC and = Draw CFIIAB, meeting...

...a triangle, and bisecting one side, bisects the other side also. 189. Cor. 2. The line which joins the middle points of two sides of a triangle is parallel to the third side, and is equal to half the third side. 190. Cor. 3. The line which is parallel to the bases of a trapezoid...