## Plane GeometryMacmillan, 1901 |

### From inside the book

Results 1-5 of 14

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**transversal**, then the angles a , b , g , and h are called exterior angles , the angles c , d , e , and f are called interior angles , the angles a and e , b and f , c and g , and d and h are called corre- sponding angles , the angles c ... Page 18

Arthur Schultze. PROPOSITION V. THEOREM 80. Two lines are parallel if a

Arthur Schultze. PROPOSITION V. THEOREM 80. Two lines are parallel if a

**transversal**to these lines makes the alternate ...**transversal**makes the alternate exterior angles equal . Ex . 50. If two sides of a triangle are 18 PLANE GEOMETRY. Page 19

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**transversal**to these lines makes the corresponding angles equal . C -D H E- B -F Hyp . CD and EF are intersected by AB in H and I respec- tively , and To prove ― ZAHD ZHIF = CD | EF . HINT . Prove the equality of a pair of alternate ... Page 20

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**transversal**AB in DHI + 2 HIF = 2 rt . Æ . To prove Proof . CD || EF . ZDHI is sup . to △ HIF , ( Hyp . ) ZEIH is ...**transversal**are supplementary . Ex . 55. Two lines are parallel if a**transversal**to these lines makes the exterior ... Page 21

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**transversal**, the al- ternate interior angles are equal . [ Converse of Prop . V. ] A B F ' F E Hyp . The parallel lines AC and DF are intersected by a**transversal**in B and E. To prove ZABE : = BEF . Proof . ABE and BEF are either equal ...### Other editions - View all

### Common terms and phrases

AABC ABCD adjacent angles algebraic altitude angle equal angle formed angles are equal apothem base angle bisect bisector central angle circumference construct a triangle decagon diagonals diagram for Prop diameter draw drawn equiangular equiangular polygon equilateral triangle equivalent exterior angle find a point Find the area given circle given line given point given triangle HINT homologous sides hypotenuse inscribed isosceles triangle joining the midpoints line joining mean proportional measured by arc median opposite sides parallel lines parallelogram perimeter perpendicular perpendicular-bisector point equidistant produced proof is left PROPOSITION prove Proof proving the equality quadrilateral radii rectangle regular hexagon regular polygon rhombus right angle right triangle SCHOLIUM School secant segments side equal similar polygons similar triangles straight angle straight line tangent THEOREM third side transversal trapezoid triangle ABC triangle are equal vertex vertical angle

### Popular passages

Page 148 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.

Page 180 - 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. B' ADC A' D' C' Hyp. In triangles ABC and A'B'C', ZA = ZA'.

Page 45 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle 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 31 - The median to the base of an isosceles triangle is perpendicular to the base.

Page 209 - The area of a regular polygon is equal to onehalf the product of its apothem and perimeter.

Page 130 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.

Page 71 - The midpoints of two opposite sides of a quadrilateral and the midpoints of the diagonals determine the vertices of a parallelogram. * Ex.

Page 26 - If one angle of a triangle is equal to the sum of the other two, the triangle can be divided into two isosceles triangles.

Page 190 - The areas of two similar triangles are to each other as the squares of any two homologous sides.

Page 56 - A line which joins the midpoints of two sides of a triangle is parallel to the third side and equal to half of it.