## A Text-book of Geometry |

### From inside the book

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Page 41

George Albert Wentworth. triangle , when one of its angles is an obtuse angle ; an acute triangle , when all three of its angles are

George Albert Wentworth. triangle , when one of its angles is an obtuse angle ; an acute triangle , when all three of its angles are

**acute angles**; an equiangular triangle , when its three angles are equal . 131. In a right triangle ... Page 42

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**acute angle**of the one equal to an**acute angle**of the other , the other**acute angles**are equal . 142. COR . 4. In a triangle there can be 42 BOOK I. PLANE GEOMETRY . Page 43

... angle , or one obtuse angle . 143. COR . 5. In a right triangle the two

... angle , or one obtuse angle . 143. COR . 5. In a right triangle the two

**acute angles**are complements of each other . 144. COR . 6. In an equiangular triangle , each angle is one- third of two right angles , or two - thirds of one right ... Page 44

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**acute angle**of the one are equal respectively to the hypote- nuse and an**acute angle**of the other . 149. COR . 2. Two right triangles are equal if a side and an**acute angle**of the one are equal respectively to a side and homologous acute ... Page 54

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**angle**is equi- distant from the sides of the**angle**. F B Ꭺ G C Let AD be the bisector of the**angle**BAC , and let 0 ...**acute**4 of the one are equal respectively to the hypotenuse and an**acute**.. OF = OG , ( homologous sides of ...### Other editions - View all

### Common terms and phrases

ABē ABCD ACē acute angle altitude angles are equal apothem base bisector bisects called centre chord circumference circumscribed circumscribed circle coincide decagon diagonal diameter divide Draw equal angles equal respectively equiangular equiangular polygon equidistant equilateral triangle exterior angles feet figure Find the area given circle given line given point given straight line given triangle greater Hence homologous sides hypotenuse inches intersect isosceles trapezoid isosceles triangle legs length line joining measured by arc middle points number of sides parallel parallelogram perimeter perpendicular prove Proof Q. E. D. Ex Q. E. D. PROPOSITION quadrilateral radii ratio rectangle regular inscribed regular polygon rhombus right angle right triangle SCHOLIUM secant segments shortest side similar polygons straight angle subtended tangent THEOREM third side trapezoid triangle ABC triangle is equal vertex vertices

### Popular passages

Page 44 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.

Page 144 - 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.

Page 130 - If four quantities are in proportion, they are in proportion by composition; that is, the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term.

Page 128 - If the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means.

Page 211 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.

Page 157 - 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 152 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.

Page 187 - ... upon the sum of two straight lines is equivalent to the sum of the squares described on the two lines plus twice their rectangle. Note. By the "rectangle of two lines" is here meant the rectangle of which the two lines are the adjacent sides.

Page 136 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.

Page 15 - LET it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line. 3.