## Plane Geometry |

### From inside the book

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**ZAOB**, where the vertex letter O is placed between the other two letters . 21. Two angles are equal if they can be made to coincide . Thus , if E can be placed upon B so that point E is on point B , line ED on line BA , and line EF on ... Page 12

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**ZAOB**+ 2 BOD ; ( b ) ≤ BOC + ≤ COD ; ( c ) ZBOC + 2 COD + 2 DOE ; - ( d ) BOE ZDOE ; -- ( e ) ≤ AOC + ≤ COD − Z BOD ; ( ƒ ) ZAOE – △ DOE - ≤ COD . 26. If one straight line meets another straight line so 12 PLANE GEOMETRY. Page 14

... straight line , and COLAB , then 1 and 2 are each right angles by § 29 ; also ,

... straight line , and COLAB , then 1 and 2 are each right angles by § 29 ; also ,

**ZAOB**is a straight angle by § 31. Hence a straight angle equals two right angles . 2 1 B A 33. Since a straight angle is equal to two right 14 PLANE GEOMETRY. Page 15

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**ZAOB**= 1st Z. Ex . 60. If ≤1 = 22 = 23 = 24 , how many degrees are there in each angle ? Ex . 61. If / 2 = 3 times 41 , 43 = ≤2 , and B 242 times 21 , how many degrees are there in each angle ? ( Use algebraic method . ) 35. The sum ... Page 19

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**ZAOB**; ( d ) ≤ COD . ( b ) ZAOC ; ( c ) △ BOE ; B 45. Problem . Construct an angle of given size at a point in a given line . Construct an angle of 35 ° at P in AB . 90 8,0 9,0 100 80 110 70 110 100 70 60 120 60 50 130 120 50 130 40 ...### Other editions - View all

### Common terms and phrases

ABCD acute angle adjacent angles adjoining figure altitude angles are equal apothem base bisector bisects central angle chord circle of radius circumscribed polygons Conclusion congruent Construct a triangle Determine diagonals diameter divide Draw drawn equal angles equal circles equal respectively equal sides equidistant equilateral triangle extended exterior angle geometry given circle given point given segment given triangle Hence homologous sides hypotenuse Hypothesis intersect isosceles trapezoid isosceles triangle length mean proportional median meeting AC mid-point Note number of sides opposite sides parallel parallelogram pentagon perigon perimeter perpendicular perpendicular-bisector PROPOSITION quadrilateral radii ratio rectangle regular inscribed polygons regular polygon rhombus right angle right triangle secant similar triangles straight angle straight line Suggestion Suggestions.-1 Supplementary Exercises tangent THEOREM trapezoid triangle ABC triangle equal Try to prove vertex ZAOB

### Popular passages

Page 166 - The sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.

Page 207 - The areas of two similar triangles are to each other as the squares of any two homologous sides.

Page 166 - The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

Page 83 - If two sides of a triangle are unequal, the angles opposite are unequal, and the greater angle is opposite the greater side.

Page 170 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.

Page 105 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.

Page 86 - If two triangles have two sides of one equal, respectively, to two sides of the other...

Page 204 - 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 299 - Prove that an equiangular polygon inscribed in a circle is regular if the number of sides is odd. Ex.

Page 194 - Two rectangles are to each other as the products of their bases and altitudes. For if R = a6, and R