The sides of a 45-45-90 triangle have the following relationship: Isosceles acute triangleĪn isosceles acute triangle is a triangle with 2 congruent sides and angles in which all the angles are acute.Īn isosceles obtuse triangle is a triangle with 2 congruent sides and angles in which the non-congruent angle is obtuse.Īn isosceles right triangle is a triangle with 2 congruent sides and angles in which the non-congruent angle measures 90°.īecause the sum of a triangle's interior angles is equal to 180°, the remaining two angles in an isosceles right triangle measure 45° (90 + 45 + 45 = 180°).Ī 45-45-90 triangle is a special type of right triangle. Also, all equilateral triangles are also classified as isosceles since they have 3 congruent sides and angles. Isosceles triangles can further be categorized as acute, obtuse, and right. Generally, triangles are categorized as acute, obtuse, right, isosceles, scalene, and equilateral. There are a few different types of isosceles triangles. The altitude drawn from the vertex angle to the base divides an isosceles triangle into two congruent right triangles.Side opposite the vertex angle is the base.So, ∠B ≅ ∠C, since corresponding parts of congruent triangles are also congruent. Based on this, △ADB ≅ △ADC by the Side-Side-Side theorem for congruent triangles since BD ≅ CD, AB ≅ AC, and AD ≅ AD. Using the Pythagorean Theorem where l is the length of the legs. ABC can be divided into two congruent triangles by drawing line segment AD, which is also the height of triangle ABC. Refer to triangle ABC below.ĪB ≅ AC so triangle ABC is isosceles. The base angles of an isosceles triangle are the same in measure. The figure below shows these parts of an isosceles triangle. The altitude from the base of an isosceles triangle to its opposite vertex divides the triangle into two congruent right triangles.
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