If a line and a plane intersect and the line is perpendicular to all lines in the plane that pass through the point of intersection.Ī segment from the vertex to the midpoint of the opposite side. If a point is equidistant from the sides of an angle, then the point lies on the bisector of the angle.ĭefinition of a line perpendicular to a plane If a point lies on the bisector of an angle, then the point is equidistant from the sides of the angle. If a point is equidistant from the endpoints of a segment, then the point lies on the perpendicular bisector of the segment. If a point lies on the perpendicular bisector of a segment, then the point is equidistant from the endpoints of the segment. If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent. If two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle, then the triangles are congruent. If two angles of a triangle are congruent, then the sides opposite those angles are congruent.Ĭorollary to the Converse of the Isosceles Triangle Theorem (Don't call it this)Īn equiangular triangle is also equilateral. The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint.Ĭonverse of the Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite those sides are congruent.Ĭorollary 1 to the Isosceles Triangle Theorem (Don't call it this!)Īn equilateral triangle is also equiangular.Ĭorollary 2 to the Isosceles Triangle Theorem (Don't call it this!)Īn equilateral triangle has three 60 degree angles.Ĭorollary 3 to the Isosceles Triangle Theorem (Don't call it this!) If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. If two sides 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 three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
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