## Plane Geometry |

### From inside the book

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Page 31

... sides and the included of one equal respectively to two sides and the included of the other , the are congruent ...

... sides and the included of one equal respectively to two sides and the included of the other , the are congruent ...

**Homologous parts**of congruent figures are parts which are similarly located ; they are the parts which coincide ... Page 32

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**homologous parts**of congruent figures are equal . Thus , in § 63 , ZC is homologous to F , and side BC is homologous to side EF . It follows that △ C F and BC = EF . Note . - = - In congruent triangles ,**homologous sides**lie opposite equal ... Page 36

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**sides**are equal . C a Α B In △ ABC , AC = BC . Hypothesis . Conclusion . LA = LB . Plan . Prove A and Proof . 1 . Let CD bisect 2 . B**homologous**...**sides**and the included equal respectively to two**sides**and the included other , the ... Page 40

... sides determine a triangle ; that is , the shape and size of the triangle cannot change unless one or more of the ...

... sides determine a triangle ; that is , the shape and size of the triangle cannot change unless one or more of the ...

**homologous parts**of congruent triangles ? Ex . 56. State Principle I. Ex . 57. What does it mean to bisect an ... Page 62

... sides and the included of one are equal respectively , etc. § 63 § 73 4. A side , the opposite △ , and another ...

... sides and the included of one are equal respectively , etc. § 63 § 73 4. A side , the opposite △ , and another ...

**homologous sides**of congruent A. § 66 F. To prove two angles equal , try to prove that they : 1. Are homologous of ...### 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