Preparation for the 8th-Grade Geometry Test

Properties of a square

1. The diagonals of a square are equal.
2. The point of intersection of the diagonals bisects them.
3. The diagonals of a square are perpendicular to each other and bisect its angles.

1. The area of a square is equal to the square of its side length.
2. Congruent figures have equal areas.
3. If a polygon is composed of several polygons, its area is equal to the sum of the areas of the polygons that compose it.
4. The area of a rectangle is equal to the product of adjacent sides; it can also be described as the product of length and width.

Values of trigonometric functions

1. $sin\mathrm{30°}=\frac{1}{2}$
   
   
2. $sin\mathrm{45°}=\frac{\sqrt{2}}{2}$
   
   
3. $sin\mathrm{60°}=\frac{\sqrt{3}}{2}$
   
   
4. $cos\mathrm{30°}=\frac{\sqrt{3}}{2}$
   
   
5. $cos\mathrm{45°}=\frac{\sqrt{2}}{2}$
   
   
6. $cos\mathrm{60°}=\frac{1}{2}$
   
   
7. $tan\mathrm{30°}=\frac{\sqrt{3}}{3}$
   
   
8. $tan\mathrm{45°}=1$
   
   
9. $tan\mathrm{60°}=\sqrt{3}$
   
   

In an equilateral triangle, the median serves as both the angle bisector and the altitude.

An inscribed angle (∠ABC) is equal to half the arc it subtends, or half the central angle (∠AOC).

For example, if arc AC measures 80°, the central angle equals the arc (also 80°), while the inscribed angle is half the arc (40°).

The similarity ratio is the ratio of corresponding sides.

Criteria for similarity

1. If two angles of one triangle are respectively equal to two angles of another triangle, then the triangles are similar.
2. If two sides of one triangle are proportional to two sides of another, and the angles between them are equal, then the triangles are similar.
3. If three sides of one triangle are proportional to three sides of another triangle, then the triangles are similar.

Properties of a rhombus

• The diagonals of a rhombus (DB and AC) are perpendicular to each other and bisect its angles, because the two triangles (BDA and BDC) are isosceles.
• Since a rhombus is a parallelogram, its diagonals (DB and AC) bisect each other at the point of intersection (O), and the median serves as both the altitude and the angle bisector.