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two figures that have the same size and shape such that their vertices can be matched up so corresponding parts ( angles and sides) of the figure are congruent
a line, ray, or segment that is perpendicular to a side of the triangle at its midpoint
distance from a point to a line
the length of the perpendicular segment from the point to the line or plane
If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
If two side and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
If two angles and the included side of one triangle are congruent to two angles and the include side of another triangle, then the triangles are congruent.
Isosceles triangle theorem
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
Corollary 1: An equilateral triangle is also equiangular
Corollary 2: An equilateral triangle has three 60 degree angles
Corollary 3: The bisector of the vertex angle of an isosceles triangle is perpendicular to the base ate its midpoint
If two angles and a non-inclulded side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent
If the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then triangles are congruent
If a point lies on the perpendicular bisector of a segment, then the point is equidistant from the endpoints of the segment
If a point is equidistant from endpoints of a segment, then the point lies on the perpendicular bisector of the segment
If a point lies on the bisector of an angle, then the point is equidistant from the sides of the angle
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