Unit 5 Quadrilaterals 5 4 Special Parallelograms S

  • Slides: 10
Download presentation
Unit 5: Quadrilaterals 5. 4: Special Parallelograms S

Unit 5: Quadrilaterals 5. 4: Special Parallelograms S

Definition: Rectangle A quadrilateral is a Rectangle has 4 right ∠s Definition: Rhombus A

Definition: Rectangle A quadrilateral is a Rectangle has 4 right ∠s Definition: Rhombus A quadrilateral is a Rhombus has 4 ≅ sides Definition: Square A quadrilateral is a Square has 4 ≅ sides and 4 right ∠s Are the following sometimes, always, or never true: 1. A rhombus is a rectangle. 2. A square is a rhombus. 3. A rectangle is a square. 4. A parallelogram is a square. 5. A square is a parallelogram.

Theorem 5 -12: Rectangle Congruent Diagonals Theorem A parallelogram is a Rectangle has ≅

Theorem 5 -12: Rectangle Congruent Diagonals Theorem A parallelogram is a Rectangle has ≅ diagonals I’ll abbreviate like this: The converse of this is also true which means… Besides the definition of rectangle, this is the main way we can prove that a parallelogram is a rectangle.

Theorem 5 -13: Rhombus Perpendicular Diagonals Thm. A parallelogram is a Rhombus has diagonals

Theorem 5 -13: Rhombus Perpendicular Diagonals Thm. A parallelogram is a Rhombus has diagonals that are ⊥ to each other I’ll abbreviate like this: Theorem 5 -14: Rhombus Diagonals Bisect Angles Thm. A parallelogram is a Rhombus has both (or either) diagonals bisecting opposite ∠s I’ll abbreviate like this: The converse of these are also true which means. . Besides the definition of rhombus, this are the 2 main ways we can prove that a parallelogram is a rhombus.

Quadrilateral Family Tree

Quadrilateral Family Tree

Remember how the diagonals of a parallelogram bisect each other? Let’s look at a

Remember how the diagonals of a parallelogram bisect each other? Let’s look at a rectangle. (Thm. 5 -15) The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices.

There are two more theorems at the bottom of p. 185. They’re mostly just

There are two more theorems at the bottom of p. 185. They’re mostly just restating our definitions for rhombus and rectangle, so we don’t need to write them on our quadrilateral family tree. Thm. 5 -16: If any 1 angle of a parallelogram is a right angle, then the parallelogram is a rectangle. Thm. 5 -17: If 2 consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus.

Statements Reasons

Statements Reasons

Quiz Review

Quiz Review

Solve for x and y.

Solve for x and y.