Triangles Flashcards
Area of a triangle
0.5* height*base
Properties for all triangles
- Sum of all angles is 180°;
- At least TWO angles is acute;
- Largest angle is opposite to largest side (ratio of sides is not equal to the ratio of angles!);
- P - Q < third side < P + Q
Pythagorean theorem
a² + b² = c²; can be used for right triangles
Pythagorean triplets
{3,4,5}, {5,12,13}, {7,24,25}, {8,15,17}
Special triplets:
{x,x,x√2}, {x,x√3,2x}
Triangle’s sides name
hypotenuse and legs
Special right triangles angles and triplets
90-30-60, {x,x√3,2x};
90-45-45, {x,x,x√2}.
Равнобедренный треугольник
Isosceles triangle
Euclid’s theorem of isosceles triangles
I. If a triangle has two equal sides, then the opposite angles must be equal.
II. If a triangle has two equal angles, then the opposite sides must be equal.
Равносторонний треугольник
Equilateral triangle
Property of equilateral triangles
Angles of equilateral triangles are always = 60°
Types of geometrical lines in triangles
altitude, perpendicular bisector, median, angle bisector
Properties of similar triangles
- Similar triangles have equal angles;
- Each angle has a corresponding one in another triangle;
- Corresponding sides are proportional
How tо prove that triangles are similar?
If triangles have two equal angles, they are similar
What is the role of a parallel segment in a triangle?
A parallel segment across a triangle automatically creates a smaller similar triangle
What is a scale factor of similar triangles?
Scale factor (k) is the result of a ratio between corresponding sides, where the larger scale quantities are in the numerator (upper).
What is the scale factor of areas of similar triangles?
To find an area of the larger triangle we multiply the area of the smaller by k²
