Math Quiz Pib - Proofs And Symmetry

The angle sum of a triangle is always 180 degrees. This is a fundamental property of triangles in Euclidean geometry. The sum of the three interior angles of any triangle will always be equal to 180 degrees.

The angle sum of a quadrilateral is always 360 degrees. This is because a quadrilateral has four angles, and the sum of the interior angles of any polygon is given by the formula (n-2) * 180, where n is the number of sides. In the case of a quadrilateral, n = 4, so the sum of the interior angles is (4-2) * 180 = 2 * 180 = 360 degrees.

The angle sum of a triangle is 180 degrees, so x = 180-30-50 = 110

The side angle to x is 180-150=30 (the angle sum is 180)
x+30 = 180 (side angles are 180)
x=150

In equilateral triangles, all sides are equal in length because the definition of an equilateral triangle is a triangle with all sides of equal length. Additionally, in equilateral triangles, all angles are equal because the sum of the angles in any triangle is always 180 degrees, and since all sides are equal, all angles must also be equal.

Use Pythagoras' theorem:

The triangle is isosceles, so the base angles are equal.

2x + 40 = 180 (angle sum)
2 x =140
x=70

In isosceles triangles, two sides are equal in length, and the two base angles are equal. However, not all sides are equal in length and not all angles are equal in isosceles triangles.

A theorem is a statement which has been mathematically proven. Theorems are not the same as definitions, as definitions provide the meaning of terms or concepts. Theorems are also not based on experiments and observations, as they are derived through logical reasoning and mathematical proof. Theorems serve as important results in mathematics, providing a foundation for further mathematical developments and applications.

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1 cm on the map is 350 000 cm in real life.
5 cm on the map is 5x350 000 cm in real life

5x350 000 = 1 750 000cm
1 750 000 / 100 = 17500 m
17500 / 1000 = 17.5 km

ANS: 17.5

a) The sum of side angles is 180 degrees, and 180-100=80
b)Vertical angles are equal (vertikalvinklar)
c) Corresponding angles are equal (likbelägna vinklar)
d) Alternate angles are equal (alternativinklar)

If it's a reduction we have a smaller number in front of a larger number.

The line k is called a bisector or bisektris, which refers to a line that divides an angle or a line segment into two equal parts.

Imagine that you are standing at the top of the figure and watching it. Then you start moving counter clockwise along the figure. How many degrees do you have to move until the figure looks exactly the same as it did from your original view? (The eye in the picture symbolises you watching the figure...)

An Italian is also a citizen of EU
An octopus can also have eight legs
If all angles are equal then the triangle is equilateral
2x8+3=19
A negative number is always less than 0
An acute angle could be anything between 0 and 90, 30 for example.
The radius is always half the diameter, and 10/2=5

Pythagoras' theorem can be used only in right angled triangles (rätvinkliga). Triangles a) b) and c) are right angled.

(Triangle c) is right angled since it is an isosceles triangle with one base angle 45 degrees, and then the other base angle must also be 45 degrees. 45+45=90 and 180-90, which means the third angle in triangle c) is 90 degrees, hence the triangle is right angled!)

It could snow in June
Equilateral triangles have equal angles
There are rich people who are very sad
4+16=20
A square is also a rectangle (all angles are 90 degrees)