What is Pythagorean Theorem?
Mathematics is a vast subject that encompasses various concepts, equations, sums, theorems. One such fundamental concept is the Pythagorean Theorem, which indeed is an important topic in the study of Mathematics. This theorem explains the relation between the sides of a right-angled triangle.
Well, what is a right-angled triangle? A right-angled triangle has one angle which is a right angle. So, the Pythagorean Theorem is basically used to determine the length of an unknown side and angle of the right-angle triangle. Also, with the help of this theorem, we can find out the formula of the base, perpendicular, and hypotenuse of the triangle.
In the next section, we will know about the Isosceles triangle, the angle, properties, and types of Isosceles triangle will also be discussed simultaneously.
Isosceles triangles are described as those triangles whose two sides are of equal measure, while the third side has a different measure.
We can understand the definition with a small activity.
- Take a rectangular sheet of paper
- Fold it in half.
- Now, draw a line starting from the top folded corner to the bottom edge. Here, you can see a triangle when you open the rectangular sheet.
- Now, mark the vertices of the triangles as P, Q, R.
- Measure PQ and OR, record the measurement.
- Now do this same activity with different measures and then observe the pattern.
- It can be observed that PQ and PR have always an equal measurement of sides.
- So, you have an Isosceles Triangle!
Out of the three angles in an Isosceles Triangle, two of its angles measure exactly the same. These same angles lie opposite to the equal sides. Thus, if the measure of an unequal angle is given in the question, then we can easily find the other two angles by the angle sum property method.
Let us look at the following example:
The measure of an unequal angle is 50°. The other two angles measure ‘x’.
Thus, as per the angle sum method:
50° + x + x = 180°
50° + 2x = 180°
2x = 180° – 50°
x = 130/2 = 65°
Thus, the measure of the other two angles in the given Isosceles Triangle is 65°.
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These are the following properties of an Isosceles Triangle:
1. The two sides are equal in this triangle, thus the side which is unequal is called the base of that triangle.
2. The angles are also equal to the two opposite equal sides of the triangle.
3. The measure of its altitude is taken from the base to the vertex (known as the topmost) of the triangle.
An isosceles triangle is being classified into three different types. They are:
1. Isosceles acute triangle – This triangle has all its angles measuring less than 90°.
2. Isosceles right triangle – This triangle has one of its angles measured exactly 90°.
3. Isosceles obtuse triangle – One of the angles in this triangle is more than 90° but less than 180°, which means one of its angles forms an obtuse angle.
Area of an Isosceles Triangle
The area of an isosceles triangle is that specific region that is occupied by two-dimensional space.
In order to calculate the area of an isosceles triangle, the following formula is used:
A = ½ × b × h square units
Thus, to calculate the area of an isosceles triangle with base and lateral side given you need to apply the Pythagorean theorem
a 2 = (b/2) 2 + h 2 Further, to have a fun and effective learning about the Pythagorean Theorem and Isosceles Triangle visit Cuemath and experience an interesting exploration of Maths and its concepts alike.