## Plane Geometry |

### From inside the book

Page 44

...

...

**triangle are unequal , the angles opposite them are unequal , and the greater**side subtends the greater angle . Given : A ABC ; AB > AC . To Prove : ACB > △ B. Proof : On AB take AR = AC . [ We may , because AB > AC . ] Draw CR and let ...### Other editions - View all

### Common terms and phrases

ABCD acute angle altitude angle adjoining angle formed apothem base bisector bisects central angle circles are tangent circumscribed circle construct a square construct a triangle described diagonals diameter divided Draw chord Draw radii equal angles equal circles equal sides equally distant equiangular polygon equilateral triangle exterior angle figure Find the area given circle given line given point given triangle Hence homologous sides hypotenuse inches inscribed angle isosceles trapezoid isosceles triangle line joining lines be drawn mean proportional measured by arc median meeting number of sides pair parallel parallelogram perimeter perpendicular point of contact produced Prove quadrilateral ratio rectangle regular polygon rhombus right angles right triangle secant segments similar polygons similar triangles square equivalent Statement straight line tangent THEOREM trapezoid triangle ABC triangles are equal vertex vertex-angle vertices

### Popular passages

Page 42 - The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

Page 148 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.

Page 79 - A circle is a plane figure bounded by a curved line, every point of which is equally distant from a point within called the center.

Page 230 - An equiangular polygon inscribed in a circle is regular (if the number of its sides is odd) . 3.

Page 43 - 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 243 - Prove that the area of an inscribed regular hexagon is a mean proportional between the areas of the inscribed and the circumscribed equilateral triangles.

Page 49 - The line joining the mid-points of two sides of a triangle is parallel to the third side, and equal to half the third side.

Page 14 - The straight lines are called the sides of the triangle, and their points of intersection are the vertices of the triangle.

Page 145 - A line parallel to one side of a triangle divides the other two sides proportionally.

Page 186 - To construct a circle which shall pass through two given points and touch a given line. Given : Points A and B ; line CD. Construction: Draw line AB meeting CD ^ P"