Special Parallelograms Section 5-4

Parallelograms We proved several things by drawing a diagonal A -- Alternate Interiors S -- Reflexive A -- Alternate Interiors 2 Congruent Triangles by ASA

Parallelograms We proved several things by drawing a diagonal Since we have congruent triangles we can prove other pieces congruent by CPCTC: 1.) Opposite Sides Congruent 2.) Opposite Angles Congruent 3.) Diagonals Bisect Each Other

If we stretch the shape to make all sides congruent… This is still a parallelogram, so diagonals bisect each other Now we have four congruent triangles by SSS

If we stretch the shape to make all sides congruent… Rhombus – a parallelogram with four congruent sides -Diagonals are perpendicular -Diagonals bisect opposite angles

Back to parallelograms We can make one of the angles 90˚ Rectangle – parallelogram with all interior angles = 90˚ -Diagonals are congruent

Diagonal Theorems Theorem 5-12 – The diagonals of a rectangle are congruent Theorem 5-13 – The diagonals of a rhombus are perpendicular Theorem 5-14 – Each diagonal of a rhombus bisects two angles of the rhombus

More Theorems 5-15 – The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices 5-16 – If one angle of a parallelogram is a right angle, then the parallelogram is a rectangle 5-17 – If two consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus.