## Elements of Plane Geometry |

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### Common terms and phrases

AABC AB² ABC and DEF AC² adjacent angles altitudes angle formed angles equal apothem arc AC arcs intercepted BC² BD² bisector chord circles are tangent circum circumference Construct a triangle COROLLARY DEFINITION Describe a circle diagonals diameter divided EFGH equal circles equally distant equiangular polygon equilateral triangle EXERCISE exterior angles figure given angle given circle given line given point hexagon homologous hypotenuse inscribed angle isosceles triangle joining the middle Let ABC Let To Prove line joining mean proportional medians meet middle points mutually equiangular opposite sides parallelogram passes perimeter perpendicular point of intersection prolonged PROPOSITION Prove ABCD Prove Proof quadrilateral radius ratio rectangle regular inscribed regular polygon rhombus right angles right-angled triangle SCHOLIUM secants segments Show similar polygons similar triangles straight line tangent THEOREM trapezoid triangle ABC unequal vertex vertical angle Whence ᎠᏴ

### Popular passages

Page 202 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.

Page 180 - In any inscribed quadrilateral, the product of the diagonals is equal to the sum of the products of the opposite sides.

Page 90 - In the same circle or in equal circles equal chords are equally distant from the center; and conversely, chords that are equally distant from the center are equal.

Page 53 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C...

Page 195 - Similar triangles are to each other as the squares of their homologous sides.

Page 30 - In an isosceles triangle the angles opposite the equal sides are equal.

Page 120 - If a quadrilateral is circumscribed about a circle, the sum of one pair of opposite sides is equal to the sum of the other pair.

Page 203 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.

Page 15 - If two triangles have two sides and the included angle of one equal respectively to two sides and the included angle of the other, the triangles are equal.

Page 72 - The lines joining the middle points of the opposite sides of a quadrilateral bisect each other.