## Plane Geometry |

### From inside the book

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Page 14

... angle into four equal parts . 3. Divide a given angle into eight equal parts . 4. Can the process of bisecting an ...

... angle into four equal parts . 3. Divide a given angle into eight equal parts . 4. Can the process of bisecting an ...

**acute angle**is an angle less than a right angle , as ≤ k . An obtuse angle is an angle greater than a right ... Page 39

... angles , the third pair of angles must be equal . The proof is left to the student . 50. Corollary 2. In any triangle there must be at least two

... angles , the third pair of angles must be equal . The proof is left to the student . 50. Corollary 2. In any triangle there must be at least two

**acute angles**. The proof is left to the student . 51. Corollary 3. — An exterior angle of ... Page 40

... angle , and one of the

... angle , and one of the

**acute angles**is four times the other , how many degrees are there in each ? 12. In a certain triangle an exterior angle is twice the adjacent interior angle , and the two opposite interior angles are equal ... Page 41

... angle between the mirrors ? SUGGESTIONS . - How many degrees are there in each angle of the triangle ? Then how many degrees are there ...

... angle between the mirrors ? SUGGESTIONS . - How many degrees are there in each angle of the triangle ? Then how many degrees are there ...

**acute angles**which have their sides perpendicular , PROOFS : PARALLEL AND PERPENDICULAR LINES 41. Page 42

... angle through the vertex , thus forming two

... angle through the vertex , thus forming two

**acute angles**. What is the relation between the**acute angles**? What is the relation between each obtuse angle and the adja- cent**acute angle**? 23. An**acute angle**and an obtuse angle which have ...### 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.