...one of the sides of another piece of cardboard. Shew that their cGs are superposed. The line joining the middle points of two sides of a triangle is parallel to the third side of the triangle and is bisected by the line joining the middle point of the third side to the opposite...

...they intercept equal parts on the transversal AC ; that is, the line DE bisects AC. 189. COR. 2. The line which joins the middle points of two sides of a triangle is para/lei to the third side, and is equal to half the third side. For, a line drawn through D, the middle...

...the centre of a parallelogram divides its perimeter into two equal parts. 35. The line which bisects two sides of a triangle is parallel to the third side, and equal to half the third side. ABAE a Fig. 3. Fig. 4. Produce (Fig. 3) DE, making EF= DE, and join BF. & DCE and BEFare...

...the centre of a parallelogram divides its perimeter into two equal parts. 35. The line which bisects two sides of a triangle is parallel to the third side, and equal to half the third side. Fig. 3. E Fig. 4. Produce (Fig. 3) DE, making EF= DE, and join BF. &, DCE and BEF are...

...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...

...(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. _/ _ \ Then BH = HC, for,...

...intercept = 0. .-. BC-DE = DE. .-. DE=iBC. QED 155. COR. 1. The line joining the middle points of tico 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/ - vC zoid, AG = GD, and GH || to AB. _/ _ \ Then BH = HC, for,...

...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 that...

...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 another triangle...

...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,...