Properties of Special Parallelograms Geometry 6.4 Properties of Special Parallelograms

Learning Targets Students 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 – 6.3 Clear desks. It is now time to take the quiz.

Vocabulary Term Name Diagram Additional Notes Rectangle Rectangle ABCD a quadrilateral with four right angles. B C A D

Vocabulary Term Name Diagram Additional Notes Rectangle Rectangle ABCD a quadrilateral with four right angles. Rhombus Rhombus ABCD A quadrilateral with four congruent sides B C A D B C A D

Vocabulary Term Name Diagram Additional Notes Rectangle Rectangle ABCD a parallelogram with four right angles. Rhombus Rhombus ABCD A parallelogram with four congruent sides Square Square ABCD - A parallelogram` with four right angles and four congruent sides B C A D B C A D B C A D

Venn Diagram Rectangle Rhombus Here is a Venn Diagram for the information today. We will be adding to this and recording it in our Quadrilateral Summary Sheet. P A R L E O G M S q u a r e Rectangle Rhombus

Always, Sometimes, or Never a. 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 Squares Parallelogram Rectangle Rhombus Square A square has the features of both rhombuses and rectangles!! Parallelogram Rectangle Rhombus Square

Example If 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 Quadrilaterals Rhombus: 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 Theorems Ex: PQRS is a rhombus. If PS = 2y + 3 and SR = 5y – 6, what is the value of y?

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

Time To Use The Theorems Example: RSTV is a rhombus. Find 𝑚∠𝑊𝑆𝑅. (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 Squares You 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 Squares You 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 Squares You 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 Squares You 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 Squares Another Try! If needed on one sheet of paper.

Practice B

Practice B

Practice B

Extra Practice

Extra Practice

Extra Practice