Lesson: 6.3 Tests for Parallelograms Objectives: To Identify the 5 CONDITIONS that GUARANTEE that a QUADRILATERAL is a PARALLELOGRAM To Use the 5 CONDITIONS to SOLVE Problems

GEOMETRY 6.3 IF a Quadrilateral is a Parallelogram THEN:

GEOMETRY 6.3 IF a Quadrilateral is a Parallelogram THEN: 1. OPPOSITE SIDES are PARALLEL

GEOMETRY 6.3 IF a Quadrilateral is a Parallelogram THEN: 1. OPPOSITE SIDES are PARALLEL 2. OPPOSITE SIDES are CONGRUENT.

GEOMETRY 6.3 IF a Quadrilateral is a Parallelogram THEN: 1. OPPOSITE SIDES are PARALLEL 2. OPPOSITE SIDES are CONGRUENT. 3. OPPOSITE ANGLES are CONGRUENT.

GEOMETRY 6.3 IF a Quadrilateral is a Parallelogram THEN: 1. OPPOSITE SIDES are PARALLEL 2. OPPOSITE SIDES are CONGRUENT. 3. OPPOSITE ANGLES are CONGRUENT. 4. CONSECUTIVE ANGLES are SUPPLEMENTARY.

GEOMETRY 6.3 IF a Quadrilateral is a Parallelogram THEN: 1. OPPOSITE SIDES are PARALLEL 2. OPPOSITE SIDES are CONGRUENT. 3. OPPOSITE ANGLES are CONGRUENT. 4. CONSECUTIVE ANGLES are SUPPLEMENTARY. 5. DIAGONALS Bisect each other.

GEOMETRY 6.3 Which, if any, of the Properties of a Parallelogram PROVE that a Quadrilateral IS a Parallelogram?

GEOMETRY 6.3 IF a QUADRILATERAL has OPPOSITE SIDES that are PARALLEL Is it a PARALLELOGRAM?

GEOMETRY 6.3 IF a QUADRILATERAL has OPPOSITE SIDES that are PARALLEL Is it a PARALLELOGRAM? YES – the DEFINITION of a PARALLELOGRAM is a Quadrilateral for which OPPOSITE SIDES are Parallel!

GEOMETRY 6.3 IF a QUADRILATERAL has ONE PAIR of OPPOSITE SIDES that are CONGRUENT, Is it a PARALLELOGRAM?

GEOMETRY 6.3 IF a QUADRILATERAL has ONE PAIR of OPPOSITE SIDES that are CONGRUENT, Is it a PARALLELOGRAM? Can you DRAW a COUNTEREXAMPLE?

GEOMETRY 6.3 IF a QUADRILATERAL has BOTH PAIR of OPPOSITE SIDES that are CONGRUENT, Is it a PARALLELOGRAM? Is there a COUNTEREXAMPLE?

GEOMETRY 6.3 IF a QUADRILATERAL has BOTH PAIR of OPPOSITE SIDES that are CONGRUENT, Is it a PARALLELOGRAM? Is there a COUNTEREXAMPLE? Can you PROVE it?

GEOMETRY 6.3 IF a QUADRILATERAL has ONE PAIR of OPPOSITE ANGLES that are CONGRUENT, Is it a PARALLELOGRAM? Is there a COUNTEREXAMPLE? Can you PROVE it?

GEOMETRY 6.3 IF a QUADRILATERAL has BOTH PAIRs of OPPOSITE ANGLES that are CONGRUENT, Is it a PARALLELOGRAM? Is there a COUNTEREXAMPLE? Can you PROVE it?

GEOMETRY 6.3 GEOMETRY 6.3 Given: Angles T and R are Congruent Angles Q and S are Congruent Prove: QRST is a Parallelogram

GEOMETRY 6.3 IF a QUADRILATERAL has DIAGONALS that Bisect each other, Is it a PARALLELOGRAM? Is there a COUNTEREXAMPLE? Can you PROVE it?

GEOMETRY 6.3

GEOMETRY 6.3 IF a QUADRILATERAL has ONE PAIR of OPPOSITE SIDES that is BOTH PARALLEL and CONGRUENT, Is it a PARALLELOGRAM? Is there a COUNTEREXAMPLE? Can you PROVE it?

GEOMETRY 6.3

GEOMETRY 6.3

GEOMETRY 6.3

GEOMETRY 6.3

GEOMETRY 6.3

GEOMETRY 6.3

GEOMETRY 6.3

GEOMETRY 6.3

GEOMETRY 6.3

COORDINATE GEOMETRY Determine whether the figure with vertices A(–3, 0), B(–1, 3), C(3, 2), and D(1, –1) is a parallelogram. Three Methods: 1. SLOPE formula 2. DISTANCE formula 3. MIDPOINT formula

Geometry 6.3 You should be able to: Determine is a Quadrilateral is a PARALLEOGRAM Determine if a CONDITION defines a PARALLELOGRAM

Lesson: 6.4 Rectangles Objectives: To Identify the PROPERTIES of RECTANGLES To Use the Rectangle Properties to SOLVE Problems To Identify the PROPERTIES of SQUARES and RHOMBI To use the Squares and Rhombi Properties to SOLVE Problems

GEOMETRY 6.4 A RECTANGLE is:

GEOMETRY 6.4 GEOMETRY 6.4 A RECTANGLE is: A QUADRILATERAL

GEOMETRY 6.4 GEOMETRY 6.4 A RECTANGLE is: A QUADRILATERAL A PARALLELOGRAM

GEOMETRY 6.4 GEOMETRY 6.4 A RECTANGLE is: A QUADRILATERAL A PARALLELOGRAM with 4 Right Angles

GEOMETRY 6.4 PROPERTIES of a Rectangle: Same as a Parallelogram

GEOMETRY 6.4 PROPERTIES of a Rectangle: Same as a Parallelogram Opposite Sides are Parallel Opposite Sides are Congruent Opposite Angles are Congruent Consecutive Sides are Supplementary Diagonals BISECT each other.

GEOMETRY 6.4 PROPERTIES of a Rectangle: Same as a Parallelogram Opposite Sides are Parallel Opposite Sides are Congruent Opposite Angles are Congruent Consecutive Sides are Supplementary Diagonals BISECT each other. All ANGLES are CONGRUENT

GEOMETRY 6.4 PROPERTIES of a Rectangle: Same as a Parallelogram Opposite Sides are Parallel Opposite Sides are Congruent Opposite Angles are Congruent Consecutive Sides are Supplementary Diagonals BISECT each other. All ANGLES are CONGRUENT DIAGONALS are

PROOF GEOMETRY 6.4 GIVEN: A B PROVE: D C DIAGONALS are

M N GEOMETRY 6.4 C Find X P O

M N GEOMETRY 6.4 GEOMETRY 6.4 GEOMETRY 6.4 C P O Find X

M N GEOMETRY 6.4 GEOMETRY 6.4 GEOMETRY 6.4 GEOMETRY 6.4 GEOMETRY 6.4 C P O Find X Find X

GEOMETRY 6.4 GEOMETRY 6.4 TRUE or FALSE? If a QUADRILATERAL has OPPOSITE SIDES that are CONGRUENT, then it is a RECTANGLE.

L K GEOMETRY 6.4 8 1 7 2 C 9 10 3 6 4 5 N M

L K GEOMETRY 6.4 GEOMETRY 6.4 8 1 7 2 C 9 10 3 6 4 5 N M

L K GEOMETRY 6.4 GEOMETRY 6.4 8 1 7 2 C 9 10 3 6 4 5 N M

Kyle is building a barn for his horse Kyle is building a barn for his horse. He measures the diagonals of the door opening to make sure that they bisect each other and they are congruent. How does he know that the measure of each corner is 90?

Quadrilateral ABCD has vertices A(–2, 1), B(4, 3), C(5, 0), and D(–1, –2). Determine whether ABCD is a rectangle. Methods: 1. Slope 2. Distance