6-6 Day 1 - Trapezoids

6-6 Day One:
Trapezoids

Trapezoid

• A quadrilateral with ONLY ONE pair of parallel sides, which are called BASES.

• Trapezoids include:

  • 2 pairs of base angles.

  • Non-parallel sides are called LEGS.

Isosceles Trapezoid

• A Trapezoid with CONGRUENT LEGS.

• Properties include:

  • Each pair of base angles are congruent.

  • Diagonals are congruent, but do NOT bisect each other.

∠D= 115, ∠E= 115, ∠F= 65

CDEF is an isosceles trapezoid where ∠C=65°. Find the values of ∠D, ∠E, and ∠F.

Example #1

Find the value of x in the isosceles trapezoid STWR.

Example #2

​**What do we know about the base angles of an isosceles trapezoid?

60 = 5x

Draw

In the diagram, PQRS is an isosceles trapezoid and the m∠R=106°. Find the angle measures of ∠Q, ∠P, and ∠S (draw your answers on the picture).

Open Ended

In Example #1, if CDEF were not an isosceles triangle would ∠C and ∠D still be supplementary? Explain in your own words.

Multiple Choice

Find the measure of ∠1.

• 86

• 48

• 132

• 94

Multiple Choice

Find the measure of ∠2.

• 86

• 48

• 132

• 94

Multiple Choice

Find the value of x in isosceles trapezoid ABCD.

• 25

• 15

• 45

• 3

Multiple Choice

Given that PQRS is an isosceles trapezoid, solve for the value of x.

• 1

• 3

• 5

• 2

In the previous chapter, we learned about midsegments of triangles... Well guess what?Trapezoids have midsegments, too!!

Midsegment of a Trapezoid

• The segment that joins the midpoints of a trapezoid's legs.

Example #3 - QR is the midsegment of trapezoid LMNP. Solve for the value of x.

​x+2 = 1/2 (4x-10+8)
x+2 = 1/2 (4x-2)
x+2 = 2x-1
+1 +1
x+3 = 2x
-x -x
3 = x

Multiple Choice

Find the midsegment.

• 14
• 28
• 12
• 16

Multiple Choice

If the quadrilateral above is a trapezoid, solve for x.

•  6.5

• 13 

•  2

•  1/2

Poll

Rank your confidence in this section from 1 to 4.

(1 = not confident, 2 = somewhat confident, 3 = confident, 4 = very confident)

• 1

• 2

• 3

• 4