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ABCD acute altitude angular points apply Euc base bisect bisectors Bookwork centre circle Construct a triangle contained describe diagonals difference distance Divide Draw a straight drawn parallel equal angles equilateral triangle EUCLID Examine exterior angles figure Find a point Find the locus fixed point formed four given line given point given square given straight line given triangle greater half Hence hypotenuse Inscribe isosceles triangle Join joining the mid-points length less Let ABC lines be drawn median meet meet BC method of Ex mid-points obtain obtuse opposite sides pair parallel parallelogram perimeter perpendicular problems produced prove quadrilateral rectangle required to prove rhombus right angles right-angled triangle Similarly solution square Standard Theorem straight line drawn trapezium Trisect vertex vertical angle
Page 81 - In every triangle, the square on the side subtending an acute angle is less than the sum of the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall on it from the opposite angle, and the acute angle.
Page 135 - PROB. from a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line : it is required to draw from the point A a straight line equal to BC.
Page 136 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Page 138 - If the square described on one side of a triangle be equal to the sum of the squares described on the other two sides, the angle contained by these two sides is a right angle.
Page 81 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side...
Page 137 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.
Page 50 - A line which joins the midpoints of two sides of a triangle is parallel to the third side and equal to half of it.
Page 137 - ... upon the same side together equal to two right angles; the two straight lines shall be parallel to one another.