What is the Formula for Area of an Isosceles Trapezoid? In a trapezoid, each side is of different lengths and the diagonals are not congruent, whereas, in an isosceles trapezoid the non-parallel sides are equal, the base angles are equal, the diagonals are congruent and the opposite angles are supplementary. What is the Difference Between a Trapezoid and an Isosceles Trapezoid? Find the Other Base Angle.Īccording to the property of an isosceles trapezoid, the base angles are equal, therefore if one base angle is 30°, then the other base angle will be equal to 30°. If One Base Angle of Isosceles Trapezoid is 30°. The two opposite sides (bases) are parallel to each other and the other two sides are equal in lengths but non-parallel to each other. In an isosceles trapezoid, the number of sides is four. What are the Properties of an Isosceles Trapezoid? The bases of an isosceles trapezoid are parallel to each other along with the legs being equal in measure. An isosceles trapezoid is a type of quadrilateral where the line of symmetry bisects one pair of the opposite sides. The apothem of a regular polygon is also the height of an isosceles triangle formed by the center and a side of the polygon, as shown in the figure below.įor the regular pentagon ABCDE above, the height of isosceles triangle BCG is an apothem of the polygon.FAQs on Isosceles Trapezoid What is an Isosceles Trapezoid?Īn isosceles trapezoid is a type of trapezoid that has nonparallel sides equal to each other. The length of the base, called the hypotenuse of the triangle, is times the length of its leg. Now in an isoceles trapezium the legs are equal ,and in this case they are in a length of 13 Now consider the diagram: Now we will have a short sypnosis of the lengths: ab23,fd12,dpfsh Now we need to find the height:In this case the height is in a right triangle. When the base angles of an isosceles triangle are 45°, the triangle is a special triangle called a 45°-45°-90° triangle. Base BC reflects onto itself when reflecting across the altitude. Leg AB reflects across altitude AD to leg AC. The altitude of an isosceles triangle is also a line of symmetry. 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. Using the Pythagorean Theorem, we can find that the base, legs, and height of an isosceles triangle have the following relationships: The height of an isosceles triangle is the perpendicular line segment drawn from base of the triangle to the opposing vertex. The angle opposite the base is called the vertex angle, and the angles opposite the legs are called base angles. Parts of an isosceles triangleįor an isosceles triangle with only two congruent sides, the congruent sides are called legs. DE≅DF≅EF, so △DEF is both an isosceles and an equilateral triangle.
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