Читать книгу Geometry for Students and Parents - Sergey D Skudaev - Страница 12

A triangle with two equal sides is called an isosceles triangle.

An isosceles triangle has many interesting properties and features:

1. If two sides of a triangle are equal, then two angles that lie opposite the equal lines are equal. Angle BAD = BCD

2. If you draw a line from the angle between two equal sides, to the middle point of the third side, that line is a bisector of the angle. See figure 23.

Figure 23. AB = BC.

Line BD is a bisector. It divides angle ABC into 2 equal angles ABD and DBC.

3. A bisector drawn from the angle between equal sides is perpendicular to the third line. It means that angle ADB and angle CDB are straight and equal 90 degrees.

An altitude drawn from the angle between equal sides is the angle bisector and a median.

AD = DC.

The two resulting triangles are equal as well.

Triangle ABD = triangle DBC.