The Ontario High School Geometry: Theoretical |
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... OF SIMILAR POLYGONS 278 CONSTRUCTIONS 280 ARCS AND ANGLES 284 ANALYSIS OF A PROBLEM - COMMON TANGENTS 285 MISCELLANEOUS EXERCISES 289 INDEX 299 THEORETICAL GEOMETRY BOOK I PRELIMINARY DEFINITIONS AND EXPLANATIONS 1. A viii CONTENTS.
... OF SIMILAR POLYGONS 278 CONSTRUCTIONS 280 ARCS AND ANGLES 284 ANALYSIS OF A PROBLEM - COMMON TANGENTS 285 MISCELLANEOUS EXERCISES 289 INDEX 299 THEORETICAL GEOMETRY BOOK I PRELIMINARY DEFINITIONS AND EXPLANATIONS 1. A viii CONTENTS.
Page 11
... common arm , and the remaining arms on opposite sides of the common arm , they are said to be adjacent angles . D A B Thus BAC and CAD are adjacent angles having the same vertex A and the common arm AC . But angles BAD and CAD , with ...
... common arm , and the remaining arms on opposite sides of the common arm , they are said to be adjacent angles . D A B Thus BAC and CAD are adjacent angles having the same vertex A and the common arm AC . But angles BAD and CAD , with ...
Page 13
... common L AED and the remainders must be equal to each other . .. L AEC Z DEB . = In the same manner it may be shown that △ AED = 4 CEB . 28. Definitions . When two angles are such that their sum is two right angles , they are said to ...
... common L AED and the remainders must be equal to each other . .. L AEC Z DEB . = In the same manner it may be shown that △ AED = 4 CEB . 28. Definitions . When two angles are such that their sum is two right angles , they are said to ...
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... common , ( Hyp . ) Z BAD = < CAD , ( Const . ) : . Δ ADB Ξ Δ ADC , ZB = Z C. ( I - 2 , page 16. ) 36. The two As ADB , ADC , in the diagram of Theo- rem 3 , are congruent , and if the isosceles A be folded along the bisector of the ...
... common , ( Hyp . ) Z BAD = < CAD , ( Const . ) : . Δ ADB Ξ Δ ADC , ZB = Z C. ( I - 2 , page 16. ) 36. The two As ADB , ADC , in the diagram of Theo- rem 3 , are congruent , and if the isosceles A be folded along the bisector of the ...
Page 24
... common , :: Δ BAD Ξ Δ CAD . BAD - Z CAD . BA = CA , AE is common , ( I — 4 , p . 22. ) and In As BAE , CAE , Z BAE = < CAE , : . Δ ΒΑΕ Ξ Δ CAE . Similarly , ABDE = △ CDE . ( I - 2 , p . 16. ) Hence , each part of the figure on one side ...
... common , :: Δ BAD Ξ Δ CAD . BAD - Z CAD . BA = CA , AE is common , ( I — 4 , p . 22. ) and In As BAE , CAE , Z BAE = < CAE , : . Δ ΒΑΕ Ξ Δ CAE . Similarly , ABDE = △ CDE . ( I - 2 , p . 16. ) Hence , each part of the figure on one side ...
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Common terms and phrases
ABē altitude base bisects centre chord circles touch circumference circumscribed common tangent concyclic Construct corresponding sides cyclic quadrilateral Describe a circle diagonals diagram diameter divided draw a st EFGH equal in area equiangular polygon equidistant equilateral exterior figure Find a point Find the locus fixed points given circle given point given st given straight line gm ABCD hypotenuse Hypothesis Hypothesis.-ABC inches inscribed circle isosceles KLMN length line drawn line joining mean proportional median drawn middle point opposite sides parallelogram perpendicular point of contact point of intersection polygon produced Proof Prove radius rect rectangle contained respectively equal rhombus right bisector secant segment Show sides equal similar square subtend tangent THEOREM triangle vertex vertices
Popular passages
Page 130 - In every triangle, the square on the side subtending either of the acute angles, is less than 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...
Page 242 - If two triangles have two sides of one proportional to two sides of the other, and the angles opposite one pair of corresponding sides...
Page 241 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 17 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another.
Page 254 - If from a point without a circle a secant and a tangent are drawn, the tangent is the mean proportional between the whole secant and its external segment.
Page 253 - When it is affirmed (for instance) that " if two straight lines in a circle intersect each other, the rectangle contained by the segments of the one is equal to the rectangle contained by the segments of the other...
Page 235 - Plot the locus of a point which moves so that the ratio of its distances from two fixed points remains constant.
Page 122 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.
Page 66 - 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 113 - TO describe a parallelogram equal to a given rectilineal figure, and having an angle equal to a given rectilineal angle.