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ABC is greater Analysis angular points base BC Bisect BC bisect the base bisectors circle construct diagonal AC distance Draw the diagonal drawn parallel Drop the perpendicular equal to half equiangular equilateral triangle exterior angles four sides given line given point given straight line given triangle greater than AC half a right Hence hypotenuse isosceles triangle joining the middle last exercise less Let ABCD Let the diagonals line joining locus meeting BC middle point opposite angles opposite sides parallel to BC parallelogram pendicular perimeter produced Prop proposition quadrilateral radius rect rectangle contained rhombus right angles right Ze right-angled triangle School Euclid segments Shew shewn equal Similarly solution square straight line drawn trapezium triangle ABC trisected vertex vertical angle Ze ABC
الصفحة 25 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
الصفحة 20 - In any triangle, if a straight line be drawn from the vertex to the middle of the base, twice the square of this line, together with twice the square of half the base, is equivalent to the sum of the squares of the other two sides of the triangle. Let...
الصفحة 39 - Show that the locus of a point such that the sum of the squares of its distances from two fixed points is constant, is a circle.
الصفحة 24 - ... exterior of two concentric circles, two straight lines be drawn touching the interior and meeting the exterior ; the distance between the points of contact will be half that between the points of intersection.
الصفحة 31 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
الصفحة 22 - ... line is bisected at the middle point of the first. 37. If through any point equidistant from two parallel straight lines, two straight lines be drawn cutting the parallel straight lines, they will intercept equal portions of these parallel straight lines. 38. If the straight line bisecting the exterior angle of a triangle be parallel to the base, shew that the triangle is isosceles. 39. Find a point B in a given straight line CD, such that if AB be drawn to B from a given point A, the angle ABC...
الصفحة 27 - Prove that the square on any straight line drawn from the vertex of an isosceles triangle to the base, is less than the square on a side of the triangle by the rectangle contained by the segments of the base : and conversely.
الصفحة 29 - The straight line drawn from the vertex of a triangle to the middle point of the base is less than half the sum of the remaining sides.