Geometry 6.4

Properties of Special ParallelogramsGeometry 6.4Learning TargetsStudents should be able to

Prove and apply properties of rectangles, rhombuses, and squares.

Use properties of rectangles, rhombuses, and squares to solve problems.Warm-up

6.1 6.3Clear desks.

It is now time to take the quiz.VocabularyTermNameDiagramAdditional NotesRectangleRectangle ABCDa quadrilateral with four right angles.

ABCDVocabularyTermNameDiagramAdditional NotesRectangleRectangle ABCDa quadrilateral with four right angles.

RhombusRhombus ABCDA quadrilateral with four congruent sides

ABCDABCDVocabularyTermNameDiagramAdditional NotesRectangleRectangle ABCDa parallelogram with four right angles.

RhombusRhombus ABCDA parallelogram with four congruent sides

SquareSquare ABCD- A parallelogram` with four right angles and four congruent sidesABCDABCDABCDVenn DiagramHere is a Venn Diagram for the information today. We will be adding to this and recording it in our Quadrilateral Summary Sheet.RectangleRhombusSquarePARALLELOGRAMAlways, Sometimes, or Nevera. A rhombus is a rectangle.b. A parallelogram is a rectangle.

c. A square is a rhombus

d. A rhombus is a parallelogram

Properties of Rectangles

Properties of Rhombuses

Properties of SquaresA square has the features of both rhombuses and rectangles!!

ParallelogramRectangleRhombusSquareExampleIf ABCD is a rectangle, what do you know about ABCD?

4 right angles (by definition of rectangle)Opposite sides are congruent and parallel (definition of parallelogram)Opposite angles are congruent (since parallelogram)Consecutive angles are supplementary (since parallelogram)Diagonals bisect each other. (since parallelogram)

Corollaries about Special QuadrilateralsRhombus:A quadrilateral is a rhombus if and only if it has four congruent sides.

Rectangle:A quadrilateral is a rectangle if and only if it has four right angles.

Square:A quadrilateral is a square if and only if it is a rhombus and a rectangle.Time To Use The TheoremsEx: PQRS is a rhombus. If PS = 2y + 3 and SR = 5y 6, what is the value of y?

Time To Use The TheoremsExample: RSTV is a rhombus. Find VT

Time To Use The Theorems

(y+2)(2y+10)Your Turn!Try on your own!Ex: In rectangle ABCD, if AB = 7x 3 and CD = 4x + 9, then find the value of x.(a) 1 (b) 2 (c) 3 (d) 4 (e) 5

Verifying Properties of SquaresYou must show that the diagonals of square ABCD are congruent perpendicular bisectors of each other. A(-1, 0), B(-3, 5), C(2, 7), D(4, 2).

Verifying Properties of SquaresYou must show that the diagonals of square ABCD are congruent perpendicular bisectors of each other. A(-1, 0), B(-3, 5), C(2, 7), D(4, 2).

Verifying Properties of SquaresYou must show that the diagonals of square ABCD are congruent perpendicular bisectors of each other. A(-1, 0), B(-3, 5), C(2, 7), D(4, 2).

Verifying Properties of SquaresYou must show that the diagonals of square ABCD are congruent perpendicular bisectors of each other. A(-1, 0), B(-3, 5), C(2, 7), D(4, 2).

Verifying Properties of SquaresAnother Try! If needed on one sheet of paper.

Practice B

Practice B

Practice B

Extra Practice

Extra Practice

Extra Practice