Congruence of two Triangles

• Two sides and the included angle equal
• Three sides equal
• Two angles and the included side equal
• (Right triangle only!) Hypotenuse and one angle equal
• (Right triangle only!) Hypotenuse and one side equal

Isosceles Triangle

• Two sides are equal
• Two base angles are equal
• The bisector of the vertex angle also bisects the base perpendicularly

Equilateral Triangle

• All sides equal
• All angles are 60 degrees
• The bisector of the vertex angle also bisects the base perpendicularly

Right Triangle

• A circle whose diameter is the hypotenuse the vertex of the right angle is on the circumference
• The center of the circle is the midpoint of the hypotenuse
• When you connect the right angle to the midpoint of the hypotenuse it's lenth is 1/2 of the hypotenuse

Parallelogram

• Opposite sides are parallel and equal
• Angles across from each other are equal
• Angles on the same side add up to 180 degrees
• The diagonals intersect at the midpoint of each

Rectangle

• (All parallelogram properties also true)
• All four angles are equal
• The diagonals are equal in length
• All angles are right angles

Rhombus

• (All parallelogram properties also true)
• All sides are equal in length
• The diagonals intersect perpendicularly

Square

• (All parallelogram, rectangle, and rhombus properties also true)
• All sides equal
• All angles are equal
• All angles are right angles
• The diagonals are equal in length and intersect perpendicularly

Dilation

• A figure with all equal angles and has sides twice as long is called a twice enlarged figure
• A figure with all equal angles and has sides half as long is called a half reduced figure
• The two figure change size but not shape

Ratio

• To find the value of a ratio divde the first number by the last number
• The proportion of a to b is ratio a:b
• When both numbers in a ratio can be multiplied or divded by the same number they are equal
• If the value of a ratio is equal the ratios are equal