| A | B |
|---|
| The Ruler Postulate | one to one correspondence between points of a line and set of real numbers such that the distance between two distinct points of the line is the absolute value of the difference of their coordinates |
| Midpoint Theorem | 2AM=AB & 2AMB=AB |
| The Protractor Postulate | half-plane with edge ray AB and any point S between A and B there exists a one-to-one correspondence between the rays that originate at S in yhr half-plane and the real numbers between 0 and 180 |
| Angle Bisector theorem | 2m angleAOX=m angel AOB, 2m angle XOB= m angle AOB |
| Linear Pair Postulate | If two angles form a linear pair then they are supplementary angles |
| SSS postulate | three sides of one triangle are congruent to three sides of another trinagl, then the two 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 two triangles are congruent |
| ASA postulate | two angles and the included side of one trinangle are congruent to two angles and the inclded sid of anouther trinangle, then the two triangles are congruent |
| AAS postulate | If two angles and the nonincluded side one triangle are congruent, to the corresponding angels and nonincluded side of another triangle, tneb the two triangles are congruent |
| LA Theorem | If a leg and an acute angle of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent |
| HA Theorem | If the hypotenuse and an acute angle of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent |
| LL Theorem | If the two legs of one right triangle are congruent to the two legs of another right 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 anouth right triangle, then the triangles are congruent |
| Isosceles triangle Theorem | If two sides of a triangle are congruent athen the angles opposite those sides are congruent |
| The Exterior Angle Thoeorem | The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle |
| The Triangle Inequality | the sum of the lengths of any two sides of a triangle is greater than the length of the third side |
| Hinge Theorem | If two sides of one triangle are congruent to two sides of a second triangle, and the included angle of the first is larger than the inclued angle of the second, then the third side of the second triangle |
| Converse of the Hinge Theorem | If two sides of one triangle are congruent to towo seides of a second triangle and the third side of the first is longer thatn the third side of the second then the included angle of the first triangle is larger than the included angle of the second triangle |
| The Midsegment Theorem | The segment that joins the midpoints of two sides of a triangle is parallel to the third side, and its length is half the length of the third side |
| SASAS theorem | two quadrilaterals are congruent if any three sides and the included angles of one are congruent to the corresponding three sieds and the included angles of the other |
| ASASA Theorem | Two quadrilaterals are congruent if any three angles and the incluede sides of th one are congruent to the three corresponding angles and the inclued angles of the other |
| AA Postulate | If two angles of one triangle are congruent to two angles of a second triangle are similar |
| SAS Theorem | If an angle of one triangle is congruent to an angle of another triangle, and the length of the sides including those angles are inproportion then the triangles are similar |
| SSS theorem | If the corresponding sides of two triangles are inproportion, then the triangles are similar |
| Triangle Proportionality Theorem | If a line parallel to one side of the triangle intersects the other two sides, then it divides those sides proportionally |
| Triangle Angle-Bisector Theorem | If a ray bisects an angle of a triangle, then it divides the opposite side into segments proportional to the onter two sides of the triangle |
| Pythagorean Theorem | In a right triangle the square of the length of the hypotenuse is equal to the sum of the squares of the legths of the legs |
| Converse of Pythagorean Theorem | If the sum the square of the lengths of two sides of a triangle is equal to the square of the length of the third side, them the triqngle is a right triangle |
| 45-45-90 degrees Theorem | In a 45-45-90 degrees triangle, the length of the hypotenuse is the square root of 2 times the lenght of a leg |
| 30-60-90 degrees Theorem | In a 30-60-90 degrees triangle, the length of the hypotenuse is twice the length of the shorter leg and the lenght of the longer leg is the square root of 3 times the length of the shorter leg |
| Area Postulate | Every polygonal region corresponds to a unique positive mumber, called the area of the region |
| Area Congruence Postulate | If two polygons are congruent then the polygonal regions determined bh them have the same area |
| Area Addition Postulate | If a region can be subdivided into nonoverlapping parts the are of the region is the sum of the areas of those nonoverlappingparts |
| area square | A=s squared |
| area rectangle | A=bh |
| area parallelogram | A=bh |
| area triangle | A=1/2 bh |
| area rhombus | A=1/2 d1 d2 |
| area of equilateral trinagle | A=s squared, square root of 3 divided by 4 |
| area trapezoid | A=h/2(b1+ b2) |
| area regular polygon | A=1/2aP |
| circumference of circle | C=pi d, C=2 pi r |
| ratio of the length of an arc to the circumference | l/C=m/360, or l=m/360(2 pi r) |
| area circle | A=pi. r squared |
