## Elementary Geometry, Plane and Solid: For Use in High Schools and Academies |

### From inside the book

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**an angle of the one equal to an angle of the other**are in the same ratio as the products of the sides containing the equal angles . B C Let BAC and B'AC " be two triangles having the angles at A equal . It is required to prove that area ... Page 231

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**an angle of the one equal to an angle of the other**are in the same ratio as the products of the sides containing the equal angles . § 309 . 5. THEOREMS ON THE AREAS OF TRIANGLES . ( 1 ) If a triangle and a parallelogram are upon the ...### Other editions - View all

Elementary Geometry, Plane and Solid; for Use in High Schools and Academies Thomas F 1859-1945 Holgate No preview available - 2018 |

Elementary Geometry Plane and Solid: For Use in High Schools and Academies Thomas F. Holgate No preview available - 2015 |

### Common terms and phrases

ABCD ACē adjacent angles altitude angle formed angles are equal apothem base bisector bisects centre chord coincide convex convex polygon COROLLARY DEFINITION diagonals diameter dicular dihedral angle draw equal angles equal in area equiangular equidistant equilateral triangle EXERCISES face angles figure given circle given line-segment given plane given point given straight line greater Hence hypotenuse identically equal interior angles isosceles triangle length Let ABC line perpendicular magnitudes measure mid-point number of sides opposite sides pair parallel planes parallelepiped parallelogram perimeter perpen plane angles point of contact point of intersection polyhedral angle polyhedron prism Proof Prop Proposition VIII pyramid quadrilateral radii radius ratio rectangle regular polygon required to prove respectively right angles right triangle segments side BC similar sphere square subtended supplementary angle surface tangent tetrahedron theorem triangle ABC triangle is equal trihedral vertex volume

### Popular passages

Page 187 - 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 230 - The formula states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the base and altitude.

Page 55 - 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 76 - The line which joins the mid-points of two sides of a triangle is parallel to the third side and equal to one half of it.

Page 43 - Prove that, if two sides of a triangle are unequal, the angle opposite the greater side is greater than the angle opposite the less.

Page 231 - A polygon of three sides is called a triangle ; one of four sides, a quadrilateral; one of five sides, a, pentagon; one of six sides, a hexagon ; one of seven sides, a heptagon ; one of eight sides, an octagon ; one of ten sides, a decagon ; one of twelve sides, a dodecagon.

Page 27 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.

Page 200 - The area of a triangle is equal to half the product of its base by its altitude.

Page 161 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.

Page 229 - Two parallelograms are similar when they have an angle of the one equal to an angle of the other, and the including sides proportional.