## Plane Geometry |

### From inside the book

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**vertex**. Thus , in the angle here represented , BA and BCare the sides and point B the**vertex**. This angle may be named " angle ABC , " or " angle B. " When using the three letters to name the angle , note that the letter at the B ... Page 11

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**vertex**. Thus ∠a is less than 2b , although their sides are represented by marks of equal lengths . C The size of ...**vertices**are together and a side of one falls along a side of the other , then observing the posi- tions of the ... Page 12

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**vertex**A of the given angle , draw an arc cutting the sides of O the given angle at the points D and E , respectively . Now with one leg at O , and without changing the opening of the compasses , draw an arc cutting the ray OP at point ... Page 13

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**vertex**B on the edge of the paper . Also mark the point N on the opposite edge of the B N C MA paper where the side BC intersects it . Then_ZMBN = ∠ABC . By using MBN another angle equal to ∠ABC may be drawn wherever desired . Use ... Page 15

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**vertex**A of the angle , and the instrument turned until the zero mark of the scale falls on the side AB . Then the point where the side AC crosses the scale shows the number of degrees in the angle . C 0 20 30 40 50 60 70 80 90 80 70 60 ...### Other editions - View all

### Common terms and phrases

ABCD AC and BC 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 diagonals diameter distance Divide a given drawn equal angles equal arcs equal circles 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 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 straight angle straight line student SUGGESTION tangent trapezoid triangle are equal vertex Write the proof Нур

### Popular passages

Page 225 - ... 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 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 132 - 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 53 - 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. 2. Two triangles are congruent if two angles and the included side of one are equal respectively to two angles and the included side of the other.

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 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 260 - 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 199 - 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.

Page 203 - In any quadrilateral the sum of the squares of the four sides is equal to the sum of the squares of the diagonals, plus four times the square of the line joining the middle points of the diagonals.

Page 47 - In a right triangle, the side opposite the right angle is called the hypotenuse and is the longest side.