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Side 52 - The diagonals of a quadrilateral intersect at right angles. Prove that the sum of the squares on one pair of opposite sides is equal to the sum of the squares on the other pair.
Side 11 - Any two sides of a triangle are together greater than the third side.
Side 47 - The six straight lines. joining two and two the centres of the four circles which touch the sides of a triangle pass each through one of the vertices of the triangle.
Side 15 - The perpendiculars from the vertices of a triangle on the opposite sides are concurrent.
Side 34 - Compare the area of the triangle formed by joining the centres of these squares with the area of the equilateral triangle.
Side 11 - The opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles, with converse.
Side 37 - If two triangles have two sides of the one equal to two sides of the...
Side 14 - Wherefore, if the ratios &c. EXERCISES. 1. Shew that the locus of the middle points of straight lines parallel to the base of a triangle and terminated by its sides is a straight line. 2. CAB, CEB are two triangles having the angle B common and the sides CA, CE equal ; if BAE be produced to D and ED be taken a third proportional to BA , AC, then the triangle BDC is similar to the triangle BAC.
Side 8 - The straight line, joining the points of bisection of two sides of a triangle, is parallel to the base.
Side 62 - If the perpendicular from any vertex of a triangle to the opposite side divides that side into two segments, how does each of these segments compare in length with its adjacent side of the triangle ? Prove it.