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Properties of isosceles triangles1/4/2024 The area of an isosceles triangle can be calculated in various ways depending on the known measures of that isosceles triangle. Now, Area of Isosceles triangle = ½ x base x height To calculate the area we can take help from this figure. The area of an isosceles angle is the total region covered by all three sides of the triangle in a 2D space. The perimeter of an isosceles triangle is the sum of all three sides.Upon drawing an altitude from the apex of an isosceles triangle it divides the triangle into two right-angle triangles.The angle which is not congruent to the other angles (base angles) is called the apex angle.And this is a theorem called Isosceles triangle base angle theorem. The two angles opposite to the equal sides are equal to each other and it is called base angles.The third side of an isosceles triangle which is unequal to the other two equal sides is called the base of the triangle.Some of the major properties are listed below: In the above image, ABC is an isosceles triangle where AB & AC sides are equal in length and the opposite angles ∠ABC & ∠ACB are equal. Angles opposite to these equal sides are also equal. Since we’ve already arrived at a unique answer in Step 3, this step is not required.An isosceles triangle is a type of triangle which has only two equal sides/angles. Step 5: Analyze Both Statements Together (if needed) Therefore, Statement 2 is not sufficient. Hence, this statement is clearly not sufficient to solve the question. However, we cannot conclude that ABC is a right-angled triangle because not every isosceles triangle is right-angled. Thus, triangle ABC is an isosceles triangle. equilateral triangle An equilateral triangle is a triangle that has all sides congruent.Using the table given above, we can see that this is a property of an isosceles triangle. Step 4: Analyze Statement 2 independently Since we could find a unique answer to the question, Statement 1 alone is sufficient.Substituting the value of ∠BAC + ∠ACB from Statement 1, we have.Using Angle Sum Property in triangle ABC, we can write:.Statement 1 tells us that ∠BAC + ∠ACB = ∠ABC Step 3: Analyze Statement 1 independently ěecause we can apply the property that we have learned from the table given above that \(AC^2 = AB^2 + BC^2\) only when ABC is a right-angled triangle.Using Pythagoras theorem, we know that the above is true if ∠ABC=\(90^o\). We can apply Pythagoras Theorem, to define the relation between perpendicular, base and hypotenuse. Commonly used as a reference side for calculating the area of the triangle. You can pick any side you like to be the base. The base of a triangle can be any one of the three sides, usually the one drawn at the bottom. The hypotenuse is the largest side and the angle opposite to it is the largest angle and measures \(90^o\). The vertex (plural: vertices) is a corner of the triangle. The Right Angled Triangle has three sides known as the perpendicular, base and hypotenuse. Hence, from the given diagram, we can say that line AD acts as a median, dividing the base BC into two equal halves, and that AD is also perpendicular to BC. In the case of an isosceles triangle, the median and the perpendicular is the same, when drawn from the vertex which joins the two equal sides. The line joining one vertex of a triangle to the midpoint of the opposite side is called a median of the triangle. Thus, if we remember this formula, it is more than enough to solve any problem related to finding the area of a triangle. The area of an equilateral triangle or any special triangle is derived from the basic formula - Area = ½ x base x height. Where a is the length of each side of the triangle. The area of any triangle can be found using the formula –įor an Equilateral triangle we sometimes use the formula given below to calculate the area quickly: (please note that in an Equilateral triangle all sides and angles are equal) (More will be discussed on this in the third section of the article) ![]() Since it can be a scalene triangle or an isosceles triangle, the value of the other two angles will depend on what kind of triangle it is. In an equilateral triangle where all sides are equal, all angles are equal to \(60^o\).Ī right-angled triangle has one of its angles as \(90^o\).In an isosceles triangle where two sides are equal, the angles opposite to the equal sides are equal.In a scalene triangle where none of the sides are equal, no two angles are equal. ![]() O All the angles of an equilateral triangle are equal.Ĭan you notice the relation between the sides and the angles? O The two angles opposite the two equal sides of an isosceles triangle are equal. O None of the angles of a scalene triangle are equal. Can you tell why can’t a right-angled triangle be an equilateral triangle?
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