A School Geometry, Parts 1-4Macmillan and Company, 1908 |
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Page x
... exterior angles at the base are equal . COR . 2. If a triangle is 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 ...
... exterior angles at the base are equal . COR . 2. If a triangle is 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 ...
Page xi
... exterior angle equal to the interior opposite angle on the same side of the cutting line ; ( iii ) the two interior angles on the same side together equal to two right angles . PARALLELS ILLUSTRATED BY ROTATION . PAGE 36 38 HYPOTHETICAL ...
... exterior angle equal to the interior opposite angle on the same side of the cutting line ; ( iii ) the two interior angles on the same side together equal to two right angles . PARALLELS ILLUSTRATED BY ROTATION . PAGE 36 38 HYPOTHETICAL ...
Page 13
... exterior angles so formed are equal . 5. In the triangle ABC the angles ABC , ACB are given equal . If AB and AC are produced beyond the base , shew that the exterior angles so formed are equal . DEFINITION . The lines which bisect an ...
... exterior angles so formed are equal . 5. In the triangle ABC the angles ABC , ACB are given equal . If AB and AC are produced beyond the base , shew that the exterior angles so formed are equal . DEFINITION . The lines which bisect an ...
Page 21
... exterior angles EBC , FCB are equal ; for they are the supplements of the equal angles at the base . E COROLLARY 2. If a triangle is equilateral , it is also equi- angular . DEFINITION . A figure is said to be symmetrical about a line ...
... exterior angles EBC , FCB are equal ; for they are the supplements of the equal angles at the base . E COROLLARY 2. If a triangle is equilateral , it is also equi- angular . DEFINITION . A figure is said to be symmetrical about a line ...
Page 28
... exterior angle is greater than either of the interior opposite angles . A Let ABC be a triangle , and let BC be produced to D. It is required to prove that the exterior LACD is greater than either of the interior opposite ABC , BAC ...
... exterior angle is greater than either of the interior opposite angles . A Let ABC be a triangle , and let BC be produced to D. It is required to prove that the exterior LACD is greater than either of the interior opposite ABC , BAC ...
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Common terms and phrases
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
Popular passages
Page 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...
Page 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.
Page 190 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Page 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.
Page 5 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Page 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.
Page 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Page 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.
Page 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.