Question

What are the basic properties of the 45-45-90 triangle?

Answer 1

Hint: We will consider the properties related to sides, angles and symmetry of the triangle. Basically 45-45-90 are given as the angles of the triangle of which after observation and studying we want to mention the properties of the triangle.

Complete step-by-step answer:
Now, explaining the question and properties we know that 45-45-90 are the angles of the triangle.
The sum of the angles of the triangle are 180.
Since we can see that the two angles are the same so we can see that it is an isosceles triangle.
So, we can also say that it has two equal sides of the triangle.
We can clearly see that the third angle is 90 that means the given triangle is a right angle triangle so we can use the properties of Pythagoras theorem.
The sides of the given triangle are in the ratio 1:1:$\sqrt{2}$ that means the hypotenuse is $\sqrt{2}$ times the side of the triangle.
We can also say that the given triangle also has one side of symmetry such as the perpendicular bisector of the base which is the hypotenuse which passes through the vertex of 90-degree angle.
It has no rotational symmetry.

Note: When this type of triangle is given in question never forget to apply the Pythagoras theorem properties as it makes the question calculation easy and helps in finding many missing values of the triangle.