## The Elements of Plane Geometry ...W.S. Sonnenschein and Company, 1884 - Geometry, Modern |

### From inside the book

Results 1-5 of 14

Page 25

... angle BAC to the angle EDF : AAA B then shall the triangles be identically equal , having the side BC equal to the side EF , the

... angle BAC to the angle EDF : AAA B then shall the triangles be identically equal , having the side BC equal to the side EF , the

**angle ACB**to the angle DFE , and the angle ABC to the angle DEF . Let the triangle ABC be applied to the ... Page 26

...

...

**angle ACB**to the angle DFF , and the angle ABC to the angle DEF . Q.E.D. Ex . 4. The straight line which bisects the vertical angle of an isosceles triangle bisects the base . Ex . 5. Any point on the bisector of the vertical angle of ... Page 27

... angles . Let ABC , DEF be two triangles having the angle ABC equal to the angle DEF , the

... angles . Let ABC , DEF be two triangles having the angle ABC equal to the angle DEF , the

**angle ACB**to the angle DFE , and the side BC to the side EF : A E then shall the triangles be identically equal , having the angle BAC equal to the ... Page 28

... angle BAC equal to the angle EDF , the side AC to the side DF , and the side AB to the side DE . Q.E.D. Ex . 10. If the bisector of an angle of a triangle is also ...

... angle BAC equal to the angle EDF , the side AC to the side DF , and the side AB to the side DE . Q.E.D. Ex . 10. If the bisector of an angle of a triangle is also ...

**angle ACB**, which is opposite to the 28 THE ELEMENTS OF PLANE GEOMETRY . Page 29

Association for the improvement of geometrical teaching. therefore the

Association for the improvement of geometrical teaching. therefore the

**angle ACB**, which is opposite to the side AB ... ACB is equal to the angle A'B'C TRIANGLES . 29.### Other editions - View all

### Common terms and phrases

AB is equal ABCD AC is equal adjacent angles adjoining sides alternate angle angle ABC angle ACB angle AFG angle BAC angle CAB angle DEF angle EDF angle FGD angles are equal angles equal BA and AC base BC bisectors bisects centre circle cutting Constr construct a triangle contrapositive diagonal equal angles equal to AC exterior angle find the locus Geometry given angle given point given straight line greater Hence hypotenuse identically equal interior opposite angle isosceles triangle less Let ABC meet middle point obtuse angle opposite sides parallel straight lines parallelogram perpendicular point equidistant Prob produced quadrilateral radius rectangle contained rectangle whose base right angles right-angled triangle shew side AB side AC side DF sides equal square on AC squares on AB straight angle straight line drawn Theorem trapezium triangle ABC triangle DEF triangles are identically twice the rectangle vertex

### Popular passages

Page 27 - 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 70 - 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 56 - ... is equal to twice as many right angles as the polygon

Page 101 - Prove that parallelograms on the same base and between the same parallels are equal in area.

Page 35 - Any two sides of a triangle are together greater than the third side.

Page 26 - The lines drawn from the extremities of the base of an isosceles triangle to the middle points of the opposite sides are equal.

Page 70 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.

Page 85 - The locus of a point at a given distance from a given point is the circumference described from the point with the given distance as radius.

Page 42 - 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 110 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.