Understanding Isosceles Right Angled Triangle
An isosceles right angled triangle is a special type of triangle where two sides are equal in length, and one angle measures exactly 90 degrees. To find all the measurements, we consider the following:
Key Characteristics
- Two Equal Sides: In an isosceles right angled triangle, the two legs (the sides forming the right angle) are of equal length. Let's denote the length of each leg as "a".
- Right Angle: The angle formed between the two equal sides is 90 degrees.
- Hypotenuse: The side opposite the right angle is the hypotenuse. It can be calculated using the Pythagorean theorem:
- Hypotenuse = √(a² + a²) = √(2a²) = a√2.
Measurements
- Angles:
- One angle = 90 degrees (right angle).
- The other two angles = 45 degrees each (since the angles in a triangle add up to 180 degrees).
- Side Lengths:
- If leg length = a, then:
- Leg 1 = a
- Leg 2 = a
- Hypotenuse = a√2
Example
- If each leg measures 5 units:
- Leg 1 = 5 units
- Leg 2 = 5 units
- Hypotenuse = 5√2 units (approximately 7.07 units)
Conclusion
To summarize, in an isosceles right angled triangle:
- There are two equal sides and one right angle.
- The angles are 90°, 45°, and 45°.
- The hypotenuse can be calculated easily from the lengths of the legs.
This understanding is essential for solving problems related to geometry in Class 6.