Chapter 4 Geometry
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Created by:
curlytopannie7 on January 10, 2012
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42 terms
Terms | 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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