![]() ![]() ![]() Knowing that an isosceles triangle has two equal sides brings us to the first isosceles triangle theorem. Frequently, a problem will employ this phrase in order to convey facts. The two parallel sides are referred to as the legs, while the third side is referred to as the foundation. Frequently, complex or sophisticated forms are deconstructed into simpler ones, such as triangles. Numerous triangles found in the real world, like a part of a slice of pizza, can be called isosceles. Properties, Characteristics, and Applications of the Isosceles Triangle Isosceles Triangle TheoremsĪccording to the isosceles triangle theorem, if two sides of a triangle are congruent, then their opposing angles are likewise congruent. This article will cover the isosceles triangle theorem and its converse. In mathematics, the isosceles triangle theorem says that the angles opposite the equal sides of an isosceles triangle are also equal in measurement. The perpendicular segment from a vertex to the line that contains the opposite side.Ī line (or segment or ray) that is perpendicular to the segment at its midpoint.An isosceles triangle has two sides of equal length and a third of varying length. 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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