A School Geometry, Teile 1-4Macmillan and Company, 1908 |
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Seite 13
... shew that the exterior angles so formed are equal . DEFINITION . The lines which bisect an angle and the adjacent ... Shew that the angles AOX and COY in the above diagram are complementary . 8 . Shew that the angles BOX and COX are ...
... shew that the exterior angles so formed are equal . DEFINITION . The lines which bisect an angle and the adjacent ... Shew that the angles AOX and COY in the above diagram are complementary . 8 . Shew that the angles BOX and COX are ...
Seite 15
... shew that OC and OD are in the same straight line . 6. Two straight lines AB , CD cross at O. If OX is the bisector ... shew that , by folding the diagram about the bisector , OA may be made to coincide with OB . How would OA fall with ...
... shew that OC and OD are in the same straight line . 6. Two straight lines AB , CD cross at O. If OX is the bisector ... shew that , by folding the diagram about the bisector , OA may be made to coincide with OB . How would OA fall with ...
Seite 19
... Shew that the bisector of the vertical angle of an isosceles triangle ( i ) bisects the base ( ii ) is perpendicular to the base . 2. Let O be the perpendicular to it . middle point of a straight line AB , and let OC be Then if P is any ...
... Shew that the bisector of the vertical angle of an isosceles triangle ( i ) bisects the base ( ii ) is perpendicular to the base . 2. Let O be the perpendicular to it . middle point of a straight line AB , and let OC be Then if P is any ...
Seite 21
... shew that = ( i ) the angle ABD the angle ADB ; ( ii ) the angle CBD the angle CDB ; ( iii ) the angle ABC = the angle ADC . 2. ABC , DBC are two isosceles triangles drawn on the same base BC , but on opposite sides of it . prove ( by ...
... shew that = ( i ) the angle ABD the angle ADB ; ( ii ) the angle CBD the angle CDB ; ( iii ) the angle ABC = the angle ADC . 2. ABC , DBC are two isosceles triangles drawn on the same base BC , but on opposite sides of it . prove ( by ...
Seite 25
... shew by a diagram that the converse is not necessarily true . ** At this stage Problems 1-5 and 8 [ see page 70 ] may conveniently be taken , the proofs affording good illustrations of the Identical Equality of Two Triangles . EXERCISES ...
... shew by a diagram that the converse is not necessarily true . ** At this stage Problems 1-5 and 8 [ see page 70 ] may conveniently be taken , the proofs affording good illustrations of the Identical Equality of Two Triangles . EXERCISES ...
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Häufige Begriffe und Wortgruppen
AB² adjacent angles altitude angle equal base BC bisector bisects circle of radius circle whose centre circles which touch circum-circle circumference circumscribed coincide common tangents concyclic Construct a triangle diagonals diagram diameter distance divided draw a circle equal in area equidistant escribed circles Euclid exterior angles Find the area find the locus given angle given circle given point given straight line given triangle greater Hence hypotenuse inches inscribed isosceles triangle length Let ABC meet metres middle point millimetre nine-points circle opposite sides orthocentre par¹ parallelogram pedal triangle perp PROBLEM produced Proof radii rect rectangle rectangle contained rectilineal figure required to prove respectively rhombus right angles right-angled triangle segment shew shewn straight line drawn tangent Theor Theorem trapezium triangle ABC triangles are equal vertex vertical angle
Beliebte Passagen
Seite xi - IF two triangles have two angles of one equal to two angles of the other, each to each ; and one side equal to one side, viz. either the sides adjacent to the equal...
Seite 44 - 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.
Seite 190 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Seite 12 - 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.
Seite 5 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Seite 122 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Seite 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Seite x - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Seite 65 - The sum of the perpendiculars from any point within an equilateral triangle to the three sides is equal to the altitude of the triangle (Fig.