## Elements of GeometryGinn and Heath, 1881 |

### From inside the book

Results 1-5 of 14

Page 37

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**ISOSCELES**. EQUILATERAL . 83. DEF . A Scalene triangle is one of which no two sides are equal . 84. DEF . An**Isosceles**triangle is one of which two sides are equal . 85. DEF . An Equilateral triangle is one of which the three sides are ... Page 46

... acute angle of the one are equal respectively to an homologous side and acute angle of the other . of the one are equal of the other ) . Q. E. D. PROPOSITION XXVIII . THEOREM . 112. In an

... acute angle of the one are equal respectively to an homologous side and acute angle of the other . of the one are equal of the other ) . Q. E. D. PROPOSITION XXVIII . THEOREM . 112. In an

**isosceles**triangle 46 BOOK 1 . GEOMETRY . Page 47

George Albert Wentworth. PROPOSITION XXVIII . THEOREM . 112. In an

George Albert Wentworth. PROPOSITION XXVIII . THEOREM . 112. In an

**isosceles**triangle the angles opposite the equal sides are equal . A 1 E B Let ABC be an**isosceles**triangle , having the sides AC and CB equal . = We are to prove LA LB ... Page 48

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**isosceles**triangle divides the triangle into two equal triangles , is perpendicular to the base , and bisects the base . C B E Let the line C E bisect the ACB of the**isosceles**ДАСВ . We are to prove I. A ACEA BCE ; II . line CEL to AB ... Page 49

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**isosceles**. A B D C In the triangle ABC , let the △ B = LC . We are to prove = AB AC . Draw A D1 to BC . In the rt . A A D B and A DC , AD = AD , ZB = LC , . ' . rt . △ A D B = rt . △ A DC , Iden . § 111 ( having a side and an acute ...### Other editions - View all

### Common terms and phrases

A B C D AABC AACB AB² ABCD adjacent angles apothem arc A B base and altitude BC² centre centre of symmetry circumference circumscribed construct a square COROLLARY decagon diagonals diameter divided Draw equal arcs equal distances equal respectively equiangular equiangular polygon equilateral equilateral polygon exterior angles figure given circle given line given polygon given square homologous sides hypotenuse intersecting isosceles Let A B Let ABC line A B measured by arc middle point number of sides parallelogram perpendicular plane polygon ABC polygon similar PROBLEM prove Q. E. D. PROPOSITION quadrilateral radii radius equal ratio rect rectangles regular inscribed regular polygon required to construct right angles right triangle SCHOLIUM segment semicircle similar polygons subtend symmetrical with respect tangent THEOREM triangle ABC vertex vertices

### Popular passages

Page 40 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.

Page 126 - To describe an isosceles triangle having each of the angles at the base double of the third angle.

Page 136 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when...

Page 207 - Construct a rectangle having the difference of its base and altitude equal to a given line, and its area equivalent to the sum of a given triangle and a given pentagon.

Page 202 - In any proportion, the product of the means is equal to the product of the extremes.

Page 142 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.

Page 175 - Any two rectangles are to each other as the products of their bases by their altitudes.

Page 72 - Every point in the bisector of an angle is equally distant from the sides of the angle ; and every point not in the bisector, but within the angle, is unequally distant from the sides of the angle.

Page 73 - A CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.

Page 146 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.