Mathews' Euclid examination papers ... on Euc. i.-iv |
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Página 126
... quadrilateral inscribed in a circle are together equal to two right angles . If the chords , which bisect two angles of a triangle inscribed in a circle , be equal , prove that either the angles are equal , or the third angle is equal ...
... quadrilateral inscribed in a circle are together equal to two right angles . If the chords , which bisect two angles of a triangle inscribed in a circle , be equal , prove that either the angles are equal , or the third angle is equal ...
Página 127
... quadrilateral a parallelogram is inscribed , whose sides are parallel to the diagonals of the quadrilateral ; prove that the diagonals of all such parallelograms intersect on the line which joins the middle points of the diagonals of ...
... quadrilateral a parallelogram is inscribed , whose sides are parallel to the diagonals of the quadrilateral ; prove that the diagonals of all such parallelograms intersect on the line which joins the middle points of the diagonals of ...
Página 129
... quadrilateral meet in E , and F is the middle point of the straight line joining the middle points of the diagonals : prove that the sum of the squares on the straight lines joining E to the angular points of the quadri- H lateral is ...
... quadrilateral meet in E , and F is the middle point of the straight line joining the middle points of the diagonals : prove that the sum of the squares on the straight lines joining E to the angular points of the quadri- H lateral is ...
Página 131
... quadrilateral inscribed in a circle are produced to meet in P , Q , and about the four triangles thus formed circles are described ; prove that the tangents to these circles at P and Q form a quadrilateral equal in all re- spects to the ...
... quadrilateral inscribed in a circle are produced to meet in P , Q , and about the four triangles thus formed circles are described ; prove that the tangents to these circles at P and Q form a quadrilateral equal in all re- spects to the ...
Página 132
... quadrilateral is divided into four equal triangles by lines joining its angular points to a point within it , prove that one of its diagonals must be bisected by the other . Fan . 1872 . 1. In any right - angled triangle , the square ...
... quadrilateral is divided into four equal triangles by lines joining its angular points to a point within it , prove that one of its diagonals must be bisected by the other . Fan . 1872 . 1. In any right - angled triangle , the square ...
Términos y frases comunes
acute angle angle contained angle equal angled triangle angular points base centre chord circle are equal circle described circumference cuts the circle Describe a square diameter draw a straight equal circles equal in area equilateral triangle exterior angle fixed circle given circle given point given square given straight line given triangle half the line hypothenuse Inscribe a circle isosceles triangle line be divided line be drawn line is equal LONDON SCHOOL BOARD London University MATRICULATION middle points Notes of Lessons obtuse angle opposite angles opposite sides parallel straight lines parallelogram are equal perpendicular point of contact proposition prove Pupil Teachers quadrilateral figure rectangle contained rectilineal figure rhombus right angles right-angled triangle segment side subtending sides containing sides equal square on half squares described straight line intercepted straight lines cut student tangents theorem third angle touch a circle triangle the square twice the rectangle vertex whole line
Pasajes populares
Página 160 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Página 154 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...
Página 184 - If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments.
Página 156 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Página 182 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Página 153 - Any two sides of a triangle are together greater than the third side.
Página 167 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Página 164 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Página 130 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Página 154 - Straight lines which are parallel to the same straight line are parallel to one another. Triangles and Rectilinear Figures. The sum of the angles of a triangle is equal to two right angles.