Lesson: 6.1 Parallelograms Pages: 291 – 294 Objectives: To Identify the PROPERTIES of QUADRILATERALS To Recognize and Apply the 5 PROPERTIES of a PARALLELOGRAM

Geometry 6.1 A QUADRILATERAL is Four-Sided POLYGON

Geometry 6.1 A QUADRILATERAL is Four-Sided POLYGON Remember: A POLYGON Is a Closed Figure Has Sides with Common Endpoints that are NOT Collinear (Unique Sides) Has Sides the INTERSECT exactly 2 Other Sides at their ENDPOINTS.

D A C B Name: Adjacent sides Opposite sides Diagonals Consecutive angles Opposite Angles

Geometry 6.1 DEFINITION: A PARALLELOGRAM is a Quadrilateral for which BOTH Pairs of Opposite Sides are PARALLEL. ABCD means parallelogram ABCD.

Geometry 6.1 D C Draw B A

Geometry 6.1 THEOREM – OPPOSITE SIDES of a Parallelogram are CONGRUENT.

D C What is TRUE about CONSECUTIVE Angles? B A

THEOREM – CONSECUTIVE ANGLES of a Parallelogram are SUPPLEMENTARY.

Geometry 6.1 D C If Opposite Sides are PARALLEL and CONGRUENT, What is TRUE about OPPOSITE ANGLES? B A

THEOREM – OPPOSITE ANGLES of a Parallelogram are CONGRUENT.

DEFINITION: A Diagonal is a SEGMENT that CONNECTS Any Two NONConsecutive Vertices.

Geometry 6.1 D C E B A What is the result of Intersecting Diagonals?

THEOREM – The DIAGONALS of a Parallelogram BISECT Each Other.

D C E A B If AE = 5, AC = _______ If BD = x + y, BE = _______ If BE = 24, EC = ________ If EC = t, AC = ________

EFGH Angle E = 9x - 3 Angle G = 8x + 6 Angle E = ?

MTRA MA = 7 Angle M = 65 TR = Angle T =

Geometry 6.1 Quadrilaterals & Parallelograms D C F E A B ABCD with Given: Prove:

Geometry 6.1 Quadrilaterals & Parallelograms SUMMARY of Properties of a Parallelogram OPPOSITE Sides of a Parallelogram are PARALLEL OPPOSITE Sides of a Parallelogram are CONGRUENT OPPOSITE Angles of a Parallelogram are CONGRUENT. CONSECUTIVE Angles of a Parallelogram are SUPPLEMENTARY DIAGONALS of a Parallelogram BISECT each other.

ABCD is a Parallelogram 15 C Yo Wo 55o Zo x B A Find the values of x, y, and z.

W 2c X WXYZ is a Parallelogram What are a,b,c and d. 15 a= b= c= d= a 18o Z 31o 22 Y

In Parallelogram ABCD, Find the measures of angles, A, B, C, and D

If RQ = 5x + 1 and QT = 3x + 15 Find QT In Parallelogram RSTV, Diagonals RT and VS intersect at Q. If RQ = 5x + 1 and QT = 3x + 15 Find QT

A B GIVEN: 1 PROVE: D E C

Geometry 6.1 You should be able to: Use PROPERTIES to Identify a QUADRILATERAL List the PROPERTIES of a PARALLELOGRAM Use Parallelogram Properties to SOLVE Problems