Lesson 5-5: Trapezoids (page 190) Essential Question How can the properties of quadrilaterals be used to solve real life problems?
a quadrilateral with exactly one pair of parallel sides. TRAPEZOID: a quadrilateral with exactly one pair of parallel sides. BASES of a TRAPEZOID : the parallel sides. LEGS of a TRAPEZOID : the non-parallel sides. base ➤ leg leg ➤ base
Trapezoid leg ➤ base ➤ base leg
ISOSCELES TRAPEZOID: a trapezoid with congruent legs. ➤ ➤
Base angles of an isosceles trapezoid are congruent . Theorem 5-18 Base angles of an isosceles trapezoid are congruent . B ➤ A ➤ X Y Proof: For an outline of this proof see page 190. Note that parallelograms are used in the proof.
Review: Median of a Triangle Median of a Trapezoid MEDIAN of a TRAPEZOID: is the segment that joins the midpoints of the legs. ● ● ● Review: Median of a Triangle Median of a Trapezoid
Theorem 5-19 The median of a trapezoid: (1) is parallel to the bases; (2) has a length equal to the average of the base lengths. Given: Trapezoid PQRS with median MN Prove: S R M N P Q Proof: For an outline of this proof see page 191. Note congruent triangles are used in the proof.
Theorem 5-19 The median of a trapezoid: (1) is parallel to the bases; (2) has a length equal to the average of the base lengths. Given: Trapezoid PQRS with median MN Prove: S ➤ R ➤ M N ➤ P Q Proof: For an outline of this proof see page 191. Note congruent triangles are used in the proof.
Theorem 5-19 The median of a trapezoid: (1) is parallel to the bases; (2) has a length equal to the average of the base lengths. Given: Trapezoid PQRS with median MN Prove: S ➤ R ➤ M N ➤ P Q Proof: For an outline of this proof see page 191. Note congruent triangles are used in the proof.
Example #1: Given a trapezoid and its median, find the value of “x”. 6 x 12
Example #2: Given a trapezoid and its median, find the value of “x”.
The QUADRILATERAL Hierarchy Parallelogram Trapezoid Rhombus Rectangle Isosceles Trapezoid Square
CHARACTERISTICS Both pairs off opposite sides are parallel Parallel- ogram Rectangle Rhombus Square Trapezoid Isosceles Trapezoid Both pairs off opposite sides are parallel Diagonals are congruent Both pairs off opposite sides are congruent At least one right angle Both pairs off opposite angles are congruent Exactly one pair of opposite sides are parallel Diagonals perpendicular Consecutive sides are congruent Consecutive angles are congruent Diagonals bisect each other Diagonals bisect opposite angles
X supp CHARACTERISTICS Both pairs off opposite sides are parallel Parallel- ogram Rectangle Rhombus Square Trapezoid Isosceles Trapezoid Both pairs off opposite sides are parallel X Diagonals are congruent Both pairs off opposite sides are congruent At least one right angle Both pairs off opposite angles are congruent Exactly one pair of opposite sides are parallel Diagonals perpendicular Consecutive sides are congruent Consecutive angles are congruent supp Diagonals bisect each other Diagonals bisect opposite angles
X supp CHARACTERISTICS Both pairs off opposite sides are parallel Parallel- ogram Rectangle Rhombus Square Trapezoid Isosceles Trapezoid Both pairs off opposite sides are parallel X Diagonals are congruent Both pairs off opposite sides are congruent At least one right angle Both pairs off opposite angles are congruent Exactly one pair of opposite sides are parallel Diagonals perpendicular Consecutive sides are congruent Consecutive angles are congruent supp Diagonals bisect each other Diagonals bisect opposite angles
X supp CHARACTERISTICS Both pairs off opposite sides are parallel Parallel- ogram Rectangle Rhombus Square Trapezoid Isosceles Trapezoid Both pairs off opposite sides are parallel X Diagonals are congruent Both pairs off opposite sides are congruent At least one right angle Both pairs off opposite angles are congruent Exactly one pair of opposite sides are parallel Diagonals perpendicular Consecutive sides are congruent Consecutive angles are congruent supp Diagonals bisect each other Diagonals bisect opposite angles
X supp CHARACTERISTICS Both pairs off opposite sides are parallel Parallel- ogram Rectangle Rhombus Square Trapezoid Isosceles Trapezoid Both pairs off opposite sides are parallel X Diagonals are congruent Both pairs off opposite sides are congruent At least one right angle Both pairs off opposite angles are congruent Exactly one pair of opposite sides are parallel Diagonals perpendicular Consecutive sides are congruent Consecutive angles are congruent supp Diagonals bisect each other Diagonals bisect opposite angles
X supp CHARACTERISTICS Both pairs off opposite sides are parallel Parallel- ogram Rectangle Rhombus Square Trapezoid Isosceles Trapezoid Both pairs off opposite sides are parallel X Diagonals are congruent Both pairs off opposite sides are congruent At least one right angle Both pairs of opposite angles are congruent Exactly one pair of opposite sides are parallel Diagonals perpendicular Consecutive sides are congruent Consecutive angles are congruent supp Diagonals bisect each other Diagonals bisect opposite angles
X supp CHARACTERISTICS Both pairs off opposite sides are parallel Parallel- ogram Rectangle Rhombus Square Trapezoid Isosceles Trapezoid Both pairs off opposite sides are parallel X Diagonals are congruent Both pairs off opposite sides are congruent At least one right angle Both pairs off opposite angles are congruent Exactly one pair of opposite sides are parallel Diagonals perpendicular Consecutive sides are congruent Consecutive angles are congruent supp Diagonals bisect each other Diagonals bisect opposite angles
Activity with cutting out shapes. Check out the tangram calendars and websites! Rearrange the 7 pieces back into a SQUARE. How can the properties of quadrilaterals be used to solve real life problems?
The tangrams can form 13 convex polygons! 1 triangle 6 quadrilaterals 2 pentagons 4 hexagons Rearrange the 7 pieces into a TRIANGLE. Rearrange the 7 pieces into a RECTANGLE. Rearrange the 7 pieces into a TRAPEZOID. Rearrange the 7 pieces into a PARALLELOGRAM.
Assignment Written Exercises on pages 192 & 193 RCOMMENDED: 1 to 9 odd numbers REQUIRED: 11 to 16 ALL numbers, 26 (NO Proof) Prepare for Quiz on Lessons 5-4 & 5-5 Tangrams Picture Project Worth 20 points PLUS possible bonus! All pictures will be judged to earn the possible bonus points. How can the properties of quadrilaterals be used to solve real life problems?
Written Exercises on page 193 What is your conclusion? CLASS Assignment Written Exercises on page 193 17 to 20 ALL numbers What is your conclusion? 21 to 25 ALL numbers & 29 How can the properties of quadrilaterals be used to solve real life problems? Continue
Prepare for Quiz on Lessons 5-4 & 5-5 Prepare for Test on Chapter 5: Quadrilaterals Tangrams Picture Project Worth 20 points PLUS possible bonus! All pictures will be judged to earn the possible bonus points. How can the properties of quadrilaterals be used to solve real life problems?