The theorem of an isosceles triangle states that in an isosceles triangle, the angles opposite to the two equal sides are equal. FAQ What is the theorem of an isosceles triangle? Understanding and applying this theorem is an important concept in geometry. It can be proven using the properties of similar triangles or the theorem of triangle congruence. This theorem can be used to solve for the angles in an isosceles triangle. The isosceles triangle theorem states that if two sides of a triangle are congruent, then the angles opposite to those two sides are also congruent. ![]() Therefore, the measure of the sides cannot be determined. What is the measure of the sides opposite to the two angles?Īnswer: Since the two angles are not equal, the triangle is not an isosceles triangle. Therefore, the measure of the angles is 53�.Ħ) In an isosceles triangle, the two angles are 65� and 75�. What is the measure of the angles opposite to the two sides?Īnswer: The angles opposite to the two sides must be congruent. Thus, the measure of the sides is 7 cm.ĥ) In an isosceles triangle, the two sides are 8 cm and 4 cm. Therefore, the measure of the sides must be equal. What is the measure of the sides opposite to the two angles?Īnswer: Since the two angles are equal, the triangle is an isosceles triangle. Therefore, the measure of the angles is 60�.Ĥ) In an isosceles triangle, the two angles are 50� and 50�. Therefore, the measure of the sides cannot be determined.ģ) In an isosceles triangle, the two sides are 7 cm and 7 cm. Therefore, the measure of the angles is 45�.Ģ) In an isosceles triangle, the two angles are 70� and 40�. Practice Problemsġ) In an isosceles triangle, the two sides are 5 cm and 7 cm. Using the isosceles triangle theorem, we can determine that the two angles of the triangle must be congruent. Consider the following example: An isosceles triangle has two sides of length 6 cm and two angles of measure x and y. ![]() The theorem can be used to solve for the angles in an isosceles triangle. Examples of the Isosceles Triangle Theorem Therefore, if two sides of a triangle are equal, then the angles opposite to those two sides must be equal. According to this theorem, if two sides of a triangle are congruent, then the angles opposite to those two sides are also congruent. The isosceles triangle theorem can also be proven using the theorem of triangle congruence. Therefore, if two angles in a triangle are the same, then the third angle must be the same as well. This is because all three angles in a triangle add up to 180�. ![]() If two sides of a triangle are congruent, then the angles opposite to those two sides must also be congruent. The theorem can be proven by using the properties of similar triangles. How to Prove the Isosceles Triangle Theorem? This theorem is used to determine the angles in an isosceles triangle, which is a triangle with two sides of equal length. ![]() The isosceles triangle theorem states that if two sides of a triangle are congruent (or equal in length), then the angles opposite to those two sides are also congruent.
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