Advanced Geometry Potulates and Theorems
there are other ones in the book, but these are the ones with names. playfair, guys.
Terms
undefined, object
copy deck
- triangle inequality theorem
- the sum of the lengths of any two sides of a triangle is greater than the length of the third side
- corresponding angles postulate (congruent)
- if two II lines are cut by a transversal, then each pair of corresponding angeles is--------
- consecutive interior angles theorem (supplementary)
- if two II lines are cut by a transversal, then each pair of consecutive interior angles is ------------
- incenter theorem
- the incenter of a triangle is equidistant from each side of the triangle
- vertical angle theorem
- if two angles are vertical angles, then they are congruent
- SAS similarity
- If the measures of two sides of a triangle are proportional to the measures of two corresponding sides of another triangle and the included angles are congruent, then the triangles are similar.
- alternate interior angles theorem (congruent)
- if two II lines are cut by a transversal, then each pair of alternate interior angles is ---------
- exterior angle inequality theorem
- if an angle is an exterior angle of a triangle then its measure is greater than the measure of either of its corresponding remote interior angles
- midpoint theorem
- if M is the midpoint of AB, the AM is congruent to MB
- compliment theorem
- if the non-common sides of two adjacent angles form a right angle, then the angles are complimentary angles
- SAS inequality theorem
- this one is too long. just look in your book- even though i didn't write it here doesn't mean its not important. p.s. the answer is SAS inequality theorem...
- AA similarity
- if the two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar
- parallel postulate
- if there is a line and a point not on that line, then there exists exactly one line through the point that is parallel to the given line
- centroid theorem
- the centroid of a triangle is located two-thirds of the distance from a vertex to the midpoint of the side opposite the vertex on a median
- protractor postulate
- given ray AB and a number r between 0 and 180, there is exactly one ray with endoint A extending on either side of ray AB, such that the measure of the angle formed is r
- postulates to prove triangles are congruent
- SSS, SAS, ASA, AAS, Hypotenuse Leg
- exterior angle theorem
- the measure of an exterior angle of a triangle has a mesure that is equal to the sum of the measures of the two remote interior angles
- angle addition postulate
- if R is the interior of angle PQS, then the measure of PQR plus the measure of RQS equals the measure of PQS. If the measure of angle PQR plus the measure of RQS equals the measure of angle PQS, then R is the interior of angle PQS. woa that was a lot.
- alternate exterior angles theorem (congruent)
- if two II lines are cut by a transversal, then each pair of alternate exterior angles is----------
- perpendicular transversal theorem
- In a plane, if a line is perpendicular to one of the two II lines, then it is perpendicular to the other
- SSS similarity
- if the measure of the corresponding sides of two triangles are proportional, then the triangles are similar
- segment addition postulate
- if B is between A and c, the AB+BC= AC. If AB+BC=AC then B is between A and C
- circumcenter theorem
- the circumcenter of a triangle is equidistant from the vertices of the triangle
- angle sum theorem
- the sum of the measure of the angles of a triangle is 180
- (no name)
- (hint: the answer to this one is "(no name)" because it has no name, although it is still important to know)any point on a the perpendicular bisector of a segment is equidistant from the endpoints of the segment
- third angle theorem
- if two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent
- SSS inequality theorem
- this one is too long. just look in your book- even though i didn't write it here doesn't mean its not important. p.s. the answer is SSS inequality theorem
- isosceles triangle theorem
- if two sides of a triangle are congruent then the angles opposite those sides are congruent
- ruler postulate
- the points on any line segment can be paired with real numbers so that, given any two points A and B on a line, A corresponds to zero, and B corresponds to a positive real number
- supplement theorem
- if two angles form a linear pair, then they are supplementary angles