8.4-8.6 Flashcards
ASA Theorem
If 2 angles & the included side of 1 angle are equal to the corresponding angles and side of another triangle, then the angles are congruent.
AAS Theorem
If two angles and a non-included side of 1 triangle are equal to corresponding angles and side of another triangle, then the triangles are equal.
ASS
ASS IZ NOT GOOD
SAS Postulate
If 2 sides & the included angle of 1 triangle are equal to the corresponding sides & angles of another triangle, then the triangles are congruent.
SSS Postulate
If 3 sides of 1 triangle are equal to the corresponding sides of another triangle, then the triangles are congruent.
angle bisector
a ray that begins in the vertex of an angle & divides the angle into 2 equal parts
segment bisector
a ray, line, or segment that divides a segment into two equal parts
perpendicular bisector
a line, ray, / seg tht bisects the seg & is perp to it
Hypotenuse-Leg Theorem
2 right triangles are equal if the hypot & leg of 1 triangle are equal to the hyp & leg of the other triangle.
isosceles triangle
a triangle w/ 2 sides = in measure
equilateral triangle
a triangle in which all the sides are equal in measure
equiangular triangle
a triangle in which all the angles are equal in measure
Isosceles Triangle Theorem
If 2 sides of a triangle of a triangle are = in measure, then the angles opp. those sides r = in msr.
Converse of Isosceles Triangle Th
If 2 angles of a triangle are equal in msr, then the sides opp those angles r = in msr
Equilateral Triangle Theorem
If a triangle is equilateral, then it’s also equiangular.
Converse of Equil Triangle Th
If a triangle is equiangular, then it’s equilateral.
Perpendicular Bisector Th
If a point is the same distance from both end points of a segment, then it lies on the perpendicular bisector of the segment.
Similar Right Triangle Th
If the altitude is drawn to the hypotenuse of a right triangle, then the 2 triangles formed are similar to each other & the original triangle.
geometric mean
If a, b, and x are positive numbers, and a/x = x/b, then x is the geometric mean b/w a and b. The gm is ALWAYS the positive root.
Geometric Mean Th
If the alt is drawn to the hypotenuse of a right triangle, then the measure of the altitude is the geometric mean b/w the measures of the parts of the hypotenuse.
If 2 angles & the included side of 1 angle are equal to the corresponding angles and side of another triangle, then the angles are congruent.
ASA Theorem
If two angles and a non-included side of 1 triangle are equal to corresponding angles and side of another triangle, then the triangles are equal.
AAS Theorem
If 2 sides & the included angle of 1 triangle are equal to the corresponding sides & angles of another triangle, then the triangles are congruent.
SAS Postulate
If 3 sides of 1 triangle are equal to the corresponding sides of another triangle, then the triangles are congruent.
SSS Postulate
2 right triangles are equal if the hypot & leg of 1 triangle are equal to the hyp & leg of the other triangle.
Hypotenuse-Leg Theorem
If 2 sides of a triangle of a triangle are = in measure, then the angles opp. those sides r = in msr.
Isosceles Triangle Theorem
If 2 angles of a triangle are equal in msr, then the sides opp those angles r = in msr
Converse of Isosceles Triangle Th
If a triangle is equilateral, then it’s also equiangular.
Equilateral Triangle Theorem
If a triangle is equiangular, then it’s equilateral.
Converse of Equil Triangle Th
If a point is the same distance from both end points of a segment, then it lies on the perpendicular bisector of the segment.
Perpendicular Bisector Th
If the altitude is drawn to the hypotenuse of a right triangle, then the 2 triangles formed are similar to each other & the original triangle.
Similar Right Triangle Th
If the alt is drawn to the hypotenuse of a right triangle, then the measure of the altitude is the geometric mean b/w the measures of the parts of the hypotenuse.
Geometric Mean Th
