## Plane Geometry |

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Plane Geometry Frank Millett Morgan,John Albert Foberg,William Edwin Breckenbridge Snippet view - 1933 |

### Common terms and phrases

ABCD adjacent sides altitude angle axis base bisector bisects called chord circle circumscribed coincides common congruent construct COROLLARY corresponding describe diagonal diameter difference distance divide Draw drawn equal equilateral EXERCISES exterior feet figure Find geometry given given circle given point greater half hypotenuse Imagine inch included inscribed intersecting isosceles triangle length less line segment mean measure median meet method mid-point miles observed opposite sides parallel parallel lines parallelogram pass perimeter perpendicular places plane polygon position PROBLEM produced Proof proportional proposition prove quadrilateral radius ratio rectangle regular polygon represent respectively right angle right triangle rotate Show sides similar solution square straight line student subtended SUGGESTION Suppose symmetric with respect symmetry tangent THEOREM third transversal trapezoid triangle unit vertex vertices

### Popular passages

Page 205 - In any triangle the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides and the cosine of their included angle.

Page 96 - The line segment joining the mid-points of two sides of a triangle is parallel to the third side and equal to one-half the length of the third side.

Page 65 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.

Page 186 - If from a point without a circle a secant and a tangent are drawn, the tangent is the mean proportional between the whole secant and its external segment.

Page 82 - ... the angle opposite the third side of the first triangle is greater than the angle opposite the third side of the second.

Page 181 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.

Page 170 - 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 185 - If two chords intersect in a circle, the product of the segments of one is equal to the product of the segments of the other.

Page 158 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.

Page 148 - 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.