...every point not in the bisector is unequally distant from the sides. 70. Theorem. The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side. 71. Theorem. A. straight line drawn parallel to the base of a...

...every point not in the bisector is unequally distant from the sides. 70. Theorem. The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side. 71. Theorem. A straight line drawn parallel to the base of a triangle,...

...(153). But this latter intercept = 0. .-. BC-DE = DE. .-. DE = £BC. QED 155. COR. 1. The line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it. 156. COR. 2. Let ABCD be a trape- D/ - <.C zoid, AG = GD, and Gil || to AB....

...parallel is terminated by the sides, or the sides produced. 66 C THEOREM (13)— The join of two mid points of two sides of a triangle is parallel to the third side, and half of it. In A ABC let D be the mid pt. of AB, and E of AC. Join DE ; and produce it to F, so...

...general, that : A straight line drawn from the middle point, etc. Corollary L 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. Corollary II. The sides of a triangle passing through the vertices of...

...middle points of the sides of a triangle perpendicular to the sides meet in a point. 2. The straight Hue which joins the middle points of two sides of a triangle is equal to half the third side. 3. Show how to bisect a triangle by a straight line drawn through one...

...perpendiculars to it from the other vertices. 4. The straight line joining the points of bisection of two sides of a triangle is parallel to the third side. 5. If a straight line be drawn through any vertex of a parallelogram so as not to intersect the parallelogram,...

...par1 to BC. QED [A second proof of this proposition may be derived from i. 38, 39.1 3. The straight line which joins the middle points of two sides of a triangle is equal to half the third side. 4. Shew that the three straight lines which join the middle points of...

...that AB, DC are parallel. So that ABCD is a parallelogram. QED Example ii. The straight line joining the middle points of two sides of a triangle is parallel to the base. Let E, F be the middle points of the sides AC, AB of the triangle ABC; it is required to prove...

...Draw DP parallel to AC. See now Proposition VII. and Proposition XXIX. 29. The straight line joining the middle points of two sides of a triangle is parallel to the third side. (v. Exercise 28.) 30. The three straight lines joining the middle points of the aides of a triangle...