Unit 7 proofs Flashcards
Definition of congruent figures
Two geometric figures are congruent if a composition of a finite number of basic rigid motions maps one figure directly onto another figure such that all points are mapped to another point.
Definition of congruent polygons
Two polygons are congruent if and only if (1) corresponding sides of those polygons are congruent and (2) all corresponding angles of those polygons are congruent.
SAS side-angle-side triangle congruence
If two sides and the angle between those sides of one triangle are congruent to two sides of another triangle, then those two triangles are congruent.
SSS side-side-side triangle congruence
If three sides of another triangle then those triangles are congruent.
ASA angle-side-angle triangle congruence
If two angles and the side between those angles of one triangle are congruent to two angles are congruent to two angles and the included side between those angles of another triangle, then those two triangles are congruent.
AAS angle-angle-side triangle congruence
If two angles and one side that is not between the angles of one triangle are congruent to two angles and one side not between those angles of another triangle then those two triangles are congruent.
SSA or ASS relationship
During our performance task, I demonstrated that the SSA relationship for triangles with acute angles allows for two possible outcomes when constructing triangles under the SSA constraints. Since this has occurred, we have never used the SSA relationship as a provable reason and used it to prove a relationship with obtuse triangles.
HL hypotenuse-leg theorem
If the hypotenuse and the leg of a right triangle are congruent to the hypotenuse and the leg of another right triangle then those triangles are congruent.
Corollary to the Isosceles triangle theorem
If a triangle is equilateral, then it is equilateral, then it is equiangular.
Converse of the Isosceles triangle theorem
If the two angles in a triangle are congruent then the sides opposite those angles are congruent.
Isosceles triangle theorem (Base angles theorem)
If a triangle is an isosceles triangle, then the angles that are across from the congruent sides are congruent.
Corollary to the converse of the isosceles triangle theorem
If a triangle is equiangular then it is equilateral.
Perpendicular Bisector Theorem
If a point is on the perpendicular bisector of a segment, then the point is equidistant from the endpoints of the segment it bisects.
Converse of the Perpendicular Bisector Theorem
If a point is equidistant from the endpoints of a segment, then the point must be on the perpendicular.
