A School Geometry, Μέρη 1-4Macmillan and Company, 1908 |
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Σελίδα x
... equilateral , it is also equiangular . THEOREM 6. [ Euc . I. 6. ] If two angles of a triangle are equal to one another , then the sides which are opposite to the equal angles are equal to one another . THEOREM 7. [ Euc . I. 8. ] If two ...
... equilateral , it is also equiangular . THEOREM 6. [ Euc . I. 6. ] If two angles of a triangle are equal to one another , then the sides which are opposite to the equal angles are equal to one another . THEOREM 7. [ Euc . I. 8. ] If two ...
Σελίδα 16
... equilateral , when all its sides are equal ; equiangular , when all its angles are equal ; regular , when it is both equilateral and equiangular 7. Triangles are thus classified with regard to their sides A triangle is said to be ...
... equilateral , when all its sides are equal ; equiangular , when all its angles are equal ; regular , when it is both equilateral and equiangular 7. Triangles are thus classified with regard to their sides A triangle is said to be ...
Σελίδα 21
... equilateral , it is also equi- angular . DEFINITION . A figure is said to be symmetrical about a line when , on being folded about that line , the parts of the figure on each side of it can be brought into coincidence . The straight ...
... equilateral , it is also equi- angular . DEFINITION . A figure is said to be symmetrical about a line when , on being folded about that line , the parts of the figure on each side of it can be brought into coincidence . The straight ...
Σελίδα 22
... to the whole ; which is absurd . .. AB is not unequal to AC ; that is , AB AC . = Theor . 4 . Q.E.D. COROLLARY . Hence if a triangle is equiangular it is also equilateral . NOTE ON THEOREMS 5 AND 6 . Theorems 5 and 22 GEOMETRY .
... to the whole ; which is absurd . .. AB is not unequal to AC ; that is , AB AC . = Theor . 4 . Q.E.D. COROLLARY . Hence if a triangle is equiangular it is also equilateral . NOTE ON THEOREMS 5 AND 6 . Theorems 5 and 22 GEOMETRY .
Σελίδα 26
... equilateral triangle is also equilateral . 9. ABC is an isosceles triangle having AB equal to AC ; and the angles at B and C are bisected by BO and CO : shew that ( i ) BO = CO ; ( ii ) AO bisects the angle BAC . 10 . Shew that the ...
... equilateral triangle is also equilateral . 9. ABC is an isosceles triangle having AB equal to AC ; and the angles at B and C are bisected by BO and CO : shew that ( i ) BO = CO ; ( ii ) AO bisects the angle BAC . 10 . Shew that the ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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...
Σελίδα 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.
Σελίδα 190 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Σελίδα 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.
Σελίδα 5 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Σελίδα 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.
Σελίδα 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Σελίδα 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.
Σελίδα 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.