Lesson: 6.6 Trapezoids Objectives: To Identify the PROPERTIES of TRAPEZOIDS To Recognize and Apply the PROPERTIES of a TRAPEZOIDS to SOLVE Problems To DEFINE a MEDIAN for a TRAPEZOID and CALCULATE its LENGTH To Identify SPECIAL PROPERTIES of ISOSCELES Trapezoids

GEOMETRY 6.6 GEOMETRY 6.6 DEFINITION -- A TRAPEZOID is a Quadrilateral with EXACTLY One Pair of PARALLEL Sides.

GEOMETRY 6.6 GEOMETRY 6.6 DEFINITION -- A TRAPEZOID is a Quadrilateral with EXACTLY One Pair of PARALLEL Sides.

GEOMETRY 6.6 GEOMETRY 6.6 DEFINITION -- A TRAPEZOID is a Quadrilateral with EXACTLY One Pair of PARALLEL Sides.

GEOMETRY 6.6 BASE -- the TWO Parallel Sides LEGS -- the TWO Nonparallel Sides Base Leg Leg Base

GEOMETRY 6.6 DEFINITION: An ISOSCELES TRAPEZOID is a Trapezoid with CONGRUENT LEGS. Base Leg Leg Base

GEOMETRY 6.6 Isosceles Trapezoid Base Angles THEOREM The BASE Angles of an isosceles Trapezoid are

GEOMETRY 6.6 Trapezoid -- Isosceles Sides Theorem If the BASE angles of a trapezoid are CONGRUENT, then the Trapezoid is

GEOMETRY 6.6 A B ? 87 ? ? D C

GEOMETRY 6.6 A B ? 5x + 3 ? 10x - 3 D C

GEOMETRY 6.6 A B 6x + 7 9x - 5 D C

GEOMETRY 6.6 Do the DIAGONALS of a Trapezoid BISECT each other?

GEOMETRY 6.6 Are the DIAGONALS of a Trapezoid CONGRUENT?

GEOMETRY 6.6 THEOREM The DIAGONALS of an ISOSCELES Trapezoid are CONGRUENT.

GEOMETRY 6.6 DEFINITION -- MEDIAN of a Trapezoid The MEDIAN of a Trapezoid is the SEGMENT that Joins the MIDPOINT of the LEGS.

A B GEOMETRY 6.6 GEOMETRY 6.6 X Y THEOREM – The MEDIAN of a Trapezoid is PARALLEL to its bases. C D

A B GEOMETRY 6.6 X Y THEOREM – The MEDIAN of a Trapezoid is PARALLEL to its bases. HALF the SUM of the LENGTHS of the Two Bases. C D

GEOMETRY 6.6 A 20 B What is CD? 15 X Y C D

GEOMETRY 6.6 A B What is AB? 19 X Y C D 13

GEOMETRY 6.6 A 28 B What is the LENGTH of the MEDIAN? X Y C 14 D

GEOMETRY 6.6 A 5X - 5 B Find XY. 3X + 6 X Y 4X - 4 C D

GEOMETRY 6.6 A 3X + 4 B Find CD. 2X + 6 X Y 4X - 13 C D

GEOMETRY 6.6 ABCD is an Isosceles Trapezoid. A B TRUE or FALSE? E AC = BD D C

U GEOMETRY 6.6 E Q QU = x2 AD = 16 Find x D F A QUAD is an Isosceles Trapezoid

U GEOMETRY 6.6 E Q QE = 17 Find AF D F A QUAD is an Isosceles Trapezoid

U GEOMETRY 6.6 E Q D F A QUAD is an Isosceles Trapezoid

GEOMETRY 6.6 ABCD is an Isosceles Trapezoid. A B Given: E 1 2 Prove: D C

B. ABCD is a quadrilateral with vertices A(5, 1), B(–3, 1), C(–2, 3), and D(2, 4). Determine whether ABCD is an isosceles trapezoid. Explain.

GEOMETRY 6.6 You should be able to: Name PROPERTIES to Identify a TRAPEZOID Name SPECIAL PROPERTIES of an ISOSCELES TRAPEZOID CALCULATE Values of Bases and MEDIANS of TRAPEZOIDS

GEOMETRY 6.6