## Chapter 4 Geometry

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curlytopannie7  on January 10, 2012

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# Chapter 4 Geometry

 Base anglean angle of an isosceles triangle opposite one of the equal sides
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#### Definitions

Base angle an angle of an isosceles triangle opposite one of the equal sides
base of an isosceles triangle the side opposite the vertex angle
CPCTC Corresponding Parts of Congruent Triangles are Congruent
corollary a practical consequence that follows naturally
Isosceles triangle a triangle with two equal sides
Legs of an isosceles triangle The congruent sides of the isosceles triangle
vertex angle The common endpoint of the rays of an angle
Polygon congruence postulate if all corresponding parts of two polygons are congruent, then the polygons are congruent
SSS postulate if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent
SAS postulate if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent
ASA postulate if two angles and the included side of one triangle are congruent to two angles and the included side of the second, the triangles are congruent
AAS theorem if two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent
HL theorem if the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent
Isosceles triangle theorem If two sides of a triangle are congruent, then the angles opposite those sides are congruent
converse of an isosceles triangle theorem If two sides of a triangle are congruent,then the sides opposite those angles are congruent
corollary a practical consequence that follows naturally
corollary a practical consequence that follows naturally
4.5.1 theorem A diagonal of a parallelogram divides the parallelogram into two congruent triangles.
4.5.2 theorem The opposite sides of a parallelogram are congruent.
4.5.3 theorem The opposite angles of a parallelogram are congruent.
4.5.4 theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other.
4.5.5 theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other.
4.5.6 theorem A rhombus is a parallelogram.
4.5.7 theorem A rectangle is a parallelogram.
4.5.8 theorem The diagonals of a rhombus are perpendicular.
4.5.9 theorem The diagonals of a rectangle are congruent.
4.5.10 theorem The diagonals of a kite are perpendicular.
4.5.11 theorem A square is a rectangle.
4.5.12 theorem A square is a rhombus.
4.5.13 theorem The diagonals of a square are congruent and are the perpendicular bisectors of each other.
4.6.1 Theorem If two pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
4.6.2 theorem If one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram.
4.6.3 theorem If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
4.6.4 theorem If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.
4.6.5 theorem A rhombus is a parallelogram.
4.6.6 theorem If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.
4.6.7 theorem If the diagonals of a parallelogram bisect the angles of the parallelogram, then the parallelogram is a rhombus.
4.6.8 theorem If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.
4.6.8 theorem If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.
4.6.9 triangle midsegment theorem A midsegment of a triangle is parallel to a side of a triangle, and its length is equal to half the length of the side.
4.8.1 betweenness postulate Q is between P and R on a line
4.8.2 triangle inequality theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

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