What are the special parallelograms?

* A Rhombus is a parallelogram with four congruent sides.
* the diagonals of a rhombus are perpendicular. the diagonals bisects the angles, and bisects each other.

* A Rectangle is a parallelogram with four congruent angles, or an Equiangular parallelogram.
* The diagonals of a rectangle are congruent and bisect each other.

*A Square is a equilateral rectangle or an equilangler rhomus.
* A Square's diagonals are congruent, perpendicular and they bisect each other.

MATH PROBLEM
The measures of the angles of a quadrilateral are x+15, 2x, x-45, and 2x-60. what types of quadrilateral could be this? 

1) parallelogram 

2) rectangle

3) Trapezoid

What are the Properties of Kites?

Kite
Two pairs of consecutive congruent sides.

Properties of Kites

• Non-vertex angles are congruent
• Vertex angles are not congruent  

• Diagonals are perpendicular
• The vertex diagonal bisects the other diagonal
• The vertex diagonal is an angle bisector of the vertex angle

How do we use Proberties of a Trapezoid?

Trapezoid
Exactly one pair of parallel sides.

Trapezoid Consecutive Angles Conjecture
the consecutive angles between the bases of a trapezoid are supplementary.

Isosceles Trapezoid Conjecture
The base angles of an isosceles trapezoid are congruent.

What are the Congruence Shortcuts?

Side-Angle-Side Triangle Postulate (SAS)
If two side of a triangle and the included angle are congruent to the two sides of another triangle and its included angle, then the two triangles are congruent.

 

• The congruent angle must be between the congruent sides.
• Triangles are congruent if any two sides and their included angle are equal in both triangles.



What are the Special Angles we can Create with Parallel lines?

Transversal
A line that intersects two or more other corresponding lines.


Corresponding Angles

Angles that are in the same position relative to the transversal and lines

• If two parallel lines are cut by a transversal, then corresponding angles are congruent.

 

Alternate Interior Angles

If two parallel lines are cut by a transversal, then alternate interior angles are congruent.



 

 





 

Alternate Exterior Angles

If two parallel lines are cut by a transversal, then alternate exterior angles are congruent.