## Plane Geometry |

### From inside the book

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**Hence**, urge the student to memorize , not only definitions , etc. , but also the exact word- ings of theorems ( not the proofs ) in the text as they are studied . In the proofs of theorems , the student should be required to give the ... Page 11

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**hence**extend without limit a b from the vertex . Thus a is less than 6 , although their sides are represented by marks of equal lengths . The size of an angle depends upon the relative directions of its sides . It may be measured by the ... Page 13

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**Hence**△ BAD = 2a + 2b . By con- tinuing the process three or more angles may be added . Also angles may be subtracted , or an angle may be multi- plied , by means of the construction in § 14 . EXERCISES 1. Draw any angle . Construct an ... Page 18

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**Hence**: I. Any two straight angles are equal . N If x and y are right angles , each is one half of a straight angle . Show the straight angles in the figure . Since a right angle is one half of a straight angle , and x halves of equals ... Page 19

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**Hence**: V. Vertical angles are equal . EXERCISES Show why y and z are ≤ Z w x D B 1. If x , in the figure of vertical angles , § 20 , is 60 ° , how many degrees are there in each of the other three angles ? Explain . 2. If one of the ...### Other editions - View all

### Common terms and phrases

AABC ABCD AC and BD acute angle altitude angle equal angles are equal apothem base bisects central angle chord circle with center circumscribed compasses and straightedge Conclusion congruent Construct a triangle Corollary corresponding sides decagon diagonals diameter distance Divide a given drawn equal angles equal arcs equal circles equidistant equilateral triangle EXERCISES exterior angles follows formed geometry given angle given circle given line given line-segment given point given triangle Hence hypotenuse Hypothesis inscribed angle intercepted internally tangent intersect isosceles triangle locus measure medians middle points number of sides parallel lines parallelogram perimeter perpendicular bisector point of contact proof in full proof is left quadrilateral radii radius ratio rectangle regular polygon rhombus right angle right triangle secant segment Show similar polygons square straight angle straight line student SUGGESTION tangent trapezoid vertex Write the proof

### Popular passages

Page 130 - If two triangles have two sides of 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.

Page 76 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.

Page 223 - ... 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 4 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the center.

Page 21 - If the first of three quantities is greater than the second, and the second is greater than the third, then the first is greater than the third.

Page 222 - Two triangles having 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.

Page 131 - ... if two triangles have two sides of one equal, respectively, to two sides of the other...

Page 72 - There are three important theorems in geometry stating the conditions under which two triangles are congruent: 1. Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the other.

Page 258 - S' denote the areas of two circles, R and R' their radii, and D and D' their diameters. Then, I . 5*1 = =»!. That is, the areas of two circles are to each other as the squares of their radii, or as the squares of their diameters.

Page 197 - 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, minus twice the product of one of these sides and the projection of the other side upon it.