Trapezoids Geometry Chapter 6 A BowerPoint Presentation

Definition of trapezoid A trapezoid is a quadrilateral with EXACTLY ONE pair of parallel sides.

Definition of trapezoid A trapezoid is a quadrilateral with EXACTLY ONE pair of parallel sides.

Parts of a trapezoid The parallel sides of the trapezoid are called bases. BASES

Parts of a trapezoid The non-parallel sides of the trapezoid are called legs. LEGS

Parts of a trapezoid There are two pairs of base angles.

Parts of a trapezoid There are two pairs of base angles. BASE ANGLES (1 st Pair)

Parts of a trapezoid There are two pairs of base angles. BASE ANGLES (1 st Pair) BASE ANGLES (2 nd Pair)

Identify bases & legs What segments are the bases? What segments are the legs?

Identify bases & legs What segments are the bases? WX & YZ What segments are the legs? XY & WZ

Geometry violence If you think about it, a trapezoid is a triangle…

Geometry violence If you think about it, a trapezoid is a triangle…that got its top chopped off!!!

Geometry violence If you think about it, a trapezoid is a triangle…that got its top chopped off!!!

Geometry violence If you think about it, a trapezoid is a triangle…that got its top chopped off!!!

Geometry violence If you think about it, a trapezoid is a triangle…that got its top chopped off!!!

Geometry violence If you think about it, a trapezoid is a triangle…that got its top chopped off!!!

Trapezoids & triangles As a result, it is not surprising that trapezoids & triangles have some similarities.

Trapezoids & triangles As a result, it is not surprising that trapezoids & triangles have some similarities. What do you call a triangle with 2 sides?

Trapezoids & triangles As a result, it is not surprising that trapezoids & triangles have some similarities. What do you call a triangle with 2 sides? What are the sides called?

Isosceles trapezoid An isosceles trapezoid has one pair of sides.

Isosceles trapezoid An isosceles trapezoid has one pair of sides. (Only legs can be. Why?)

Isosceles triangles & trapezoids In isosceles triangle ABC, B is a vertex. What are A & C called?

Isosceles triangles & trapezoids What do you know about A & C ?

If isosceles trapezoid, then each pair of base s

If one pair of base s in a trapezoid, then isosceles trapezoid

Trapezoid is isosceles IF AND ONLY IF diagonals congruent

If WY XZ then WXYZ is isosceles trapezoid

Trapezoid is isosceles IF AND ONLY IF diagonals congruent If WY XZ then WXYZ is isosceles trapezoid

Think about it… It is possible for WY XZ. Can WY and XZ bisect each other?

Midsegment of a triangle Remember that the midsegment of a triangle connects the midpoints of two sides.

Midsegment of a triangle Remember that the midsegment of a triangle connects the midpoints of two sides.

Midsegment of a triangle It is always parallel to the third side.

Midsegment of a triangle Do you remember the relationship between the length of the third side and the length of the midsegment?

Midsegment of a triangle Do you remember the relationship between the length of the third side and the length of the midsegment? x 30 What is the value of x?

Midsegment of a triangle Do you remember the relationship between the length of the third side and the length of the midsegment? x 30 What is the value of x? (x = 15)

Midsegment of a triangle Do you remember the relationship between the length of the third side and the length of the midsegment? x 20 What is the value of x?

Midsegment of a triangle Do you remember the relationship between the length of the third side and the length of the midsegment? x 20 What is the value of x? (x = 40)

Midsegment of a triangle Midsegment = (Length of 3 rd side) or 2 (Midsegment) = Length of 3 rd side 9 18

Midsegment of a trapezoid The midsegment of a trapezoid connects the midpoints of the two legs

Trapezoid Midsegment Theorem Two things happen in the Trapezoid Midsegment Theorem…

Trapezoid Midsegment Theorem #1 – The midsegment is parallel to both bases

Trapezoid Midsegment Theorem #1 – The midsegment is parallel to both bases

Trapezoid Midsegment Theorem #2 – The length of the midsegment equals the average length of the bases

Trapezoid Midsegment Theorem #2 – The length of the midsegment equals the average length of the bases x 16 8

Trapezoid Midsegment Theorem #2 – The length of the midsegment equals the average length of the bases x =

Trapezoid Midsegment Theorem

Solve for x x 45 27

Trapezoid Midsegment Theorem Solve for x x (x = 36)

Trapezoid Midsegment Theorem Solve for x 24 x 11

Trapezoid Midsegment Theorem Solve for x 24 x 11 (x = 37)