A Text-book of Geometrical DeductionsLongmans, Green and Company, 1891 - Geometry |
From inside the book
Results 1-5 of 38
Page
... right angles to or is perpen- " " " " 99 دو وو 19 " " rt . L 99 AB2 99 AB CD 39 AB - CD " " dicular to . is parallel to . is greater than . is less than . together with . diminished by . triangle . angle . right angle . parallelogram ...
... right angles to or is perpen- " " " " 99 دو وو 19 " " rt . L 99 AB2 99 AB CD 39 AB - CD " " dicular to . is parallel to . is greater than . is less than . together with . diminished by . triangle . angle . right angle . parallelogram ...
Page 2
... angle of an isosceles triangle bisects the base , and is at right angles to the base . A Show , as in above proof , that and hence ( 1 ) △ BADE A CAD , BD = CD , ( 2 ) LADB = LADC = rt . 4. [ Def . of rt . . 3. ABC is an isosceles ...
... angle of an isosceles triangle bisects the base , and is at right angles to the base . A Show , as in above proof , that and hence ( 1 ) △ BADE A CAD , BD = CD , ( 2 ) LADB = LADC = rt . 4. [ Def . of rt . . 3. ABC is an isosceles ...
Page 3
... angles and the two in- cluded sides of the one respectively equal to the corresponding angles and sides of the other , they shall be equal in all respects . Use superposition . 8. If AB , or AB produced , bisect CD at right angles ...
... angles and the two in- cluded sides of the one respectively equal to the corresponding angles and sides of the other , they shall be equal in all respects . Use superposition . 8. If AB , or AB produced , bisect CD at right angles ...
Page 6
... right angles . Observe that the diagonal which joins the vertices of the isosceles triangles divides the kite into two con- gruent triangles , and that it also bisects the other diagonal . 3. The opposite angles of a rhombus are equal ...
... right angles . Observe that the diagonal which joins the vertices of the isosceles triangles divides the kite into two con- gruent triangles , and that it also bisects the other diagonal . 3. The opposite angles of a rhombus are equal ...
Page 7
... right angles to each other . Show , as in Ex . 3 , that L BAC = ✩ DAC . Compare As BAO , DAO . B Observe that this ... right angles to each other , and ( 4 ) bisect the angles of the square . For ( 1 ) show by Euc . I. 4 that A BADA ABC ...
... right angles to each other . Show , as in Ex . 3 , that L BAC = ✩ DAC . Compare As BAO , DAO . B Observe that this ... right angles to each other , and ( 4 ) bisect the angles of the square . For ( 1 ) show by Euc . I. 4 that A BADA ABC ...
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A Text-Book of Geometrical Deductions: Book I. Corresponding to ..., Book 1 James Blaikie,W. Thomson No preview available - 2017 |
Common terms and phrases
26 to show 38 to show ABCD altitude angle equal angular points apply Euc bisect bisectors Bookwork centre Compare Ex Construct a right-angled Construct a triangle Construct an isosceles convex polygon diagonals Draw a straight drawn parallel equal angles equilateral triangle EUCLID exterior angles Find a point Find the locus fixed point given line given point given square given straight line given the base given triangle hypotenuse isosceles triangle joining the mid-points LADC Let ABC line which joins lines be drawn median meet BC method of Ex mid-point of BC obtuse opposite angles opposite sides parallel straight lines parallelogram perimeter point in BC previous Ex quadrilateral quadrilateral ABCD rectangle required to prove respectively equal rhombus right angles right-angled triangle satisfies the condition Standard Theorem straight line drawn trapezium triangle required Trisect vertex vertical angle
Popular passages
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 27 - If two triangles have two sides of the one equal to two sides of the...
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.
Page 135 - The angles at the base of an isosceles triangle are equal to one another; and if the equal sides be produced the angles on the other side of the base shall be equal to one another.