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geometry midterm2011
| Question | Answer |
|---|---|
| Reflexive Property | A quantity is congruent (equal) to itself. a = a |
| Symmetric Property | If a = b, then b = a. |
| Transitive Property | If a = b and b = c, then a = c. |
| Addition Postulate | If equal quantities are subtracted from equal quantities, the differences are equal. |
| Subtraction Postulate | If equal quantities are subtracted from equal quantities, the differences are equal. |
| Multiplication Postulate | If equal quantities are multiplied by equal quantities, the products are equal. (also Doubles of equal quantities are equal.) |
| Division Postulate | If equal quantities are divided by equal nonzero quantities, the quotients are equal. (also Halves of equal quantities are equal.) |
| Substitution Postulate | A quantity may be substituted for its equal in any expression. |
| Partition Postulate | The whole is equal to the sum of its parts. |
| Angle Addition Postulate | m |
| Construction | Two points determine a straight line. |
| Right Angles | All right angles are congruent. |
| Straight Angles | All straight angles are congruent. |
| Congruent Supplements | Supplements of the same angle, or congruent angles, are congruent. |
| Congruent Complements | Complements of the same angle, or congruent angles, are congruent. |
| Linear Pair | If two angles form a linear pair, they are supplementary. |
| Vertical Angles | Vertical angles are congruent. |
| Triangle Sum | The sum of the interior angles of a triangle is 180ยบ. |
| Exterior Angle | The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. The measure of an exterior angle of a triangle is greater than either non-adjacent interior angle. |
| Base Angle Theorem (Isosceles Triangle) | If two sides of a triangle are congruent, the angles opposite these sides are congruent. |
| Base Angle Converse (Isosceles Triangle) | If two angles of a triangle are congruent, the sides opposite these angles are congruent. |
| Side-Side-Side (SSS) Congruence | If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. |
| Side-Angle-Side (SAS) Congruence | If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. |
| Angle-Side-Angle (ASA) Congruence | If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. |
| Angle-Angle-Side (AAS) Congruence | If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. |
| Hypotenuse-Leg (HL) Congruence (right triangle) | If the hypotenuse and leg of one right triangle are congruent to the corresponding parts of another right triangle, the two right triangles are congruent. |
| CPCTC | Corresponding parts of congruent triangles are congruent. |
| Angle-Angle (AA) Similarity | If two angles of one triangle are congruent to two angles of another triangle, the triangles are similar. |
| SSS for Similarity | If the three sets of corresponding sides of two triangles are in proportion, the triangles are similar. |
| SAS for Similarity | If an angle of one triangle is congruent to the corresponding angle of another triangle and the lengths of the sides including these angles are in proportion, the triangles are similar. |
| Side Proportionality | If two triangles are similar, the corresponding sides are in proportion. |
| Mid-segment Theorem (also called mid-line) | The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long. |
| Sum of Two Sides | The sum of the lengths of any two sides of a triangle must be greater than the third side |
| Longest Side | In a triangle, the longest side is across from the largest angle. In a triangle, the largest angle is across from the longest side. |
| Altitude Rule | The altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse. |
| Leg Rule | Each leg of a right triangle is the mean proportional between the hypotenuse and the projection of the leg on the hypotenuse. |
| Corresponding Angles | If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. |
| Corresponding Angles Converse | If two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel. |
| Alternate Interior Angles | If two parallel lines are cut by a transversal, then the alternate interior angles are congruent. |
| Alternate Exterior Angles | If two parallel lines are cut by a transversal, then the alternate exterior angles are congruent. |
| Interiors on Same Side | If two parallel lines are cut by a transversal, the interior angles on the same side of the transversal are supplementary. |
| Alternate Interior Angles Converse | If two lines are cut by a transversal and the alternate interior angles are congruent, the lines are parallel. |
| Alternate Exterior AnglesConverse | If two lines are cut by a transversal and the alternate exterior angles are congruent, the lines are parallel. |
| Interiors on Same Side Converse | If two lines are cut by a transversal and the interior angles on the same side of the transversal are supplementary, the lines are parallel. |
| geometric mean | x=square root(ab) |
| 30 60 90 | X, 2X, Xsquare root of 3 |
| 45 45 90 | square root of 2 over 2 |
| vertical angles | across |
Created by:
adeleverrengia
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