Download Geometry Ms. Gong Feb.18-Note 6.6 Trapezoids and Kites (2)

Geometry
Ms. Gong
Feb.18-Note
6.6 Trapezoids and Kites (2)
Objective: SWBAT verify and use properties of trapezoids.
1. Definition –Trapezoids
A trapezoid is a quadrilateral ___________
____.
2. Definition –Isosceles Trapezoids
An isosceles trapezoid is a trapezoid with ______
____.
___________
____.
3. Investigation –Theorem 6-19
Direction
Isosceles trapezoid FGHK is shown to the right. How is it different than trapezoid ABCD?
Legs are
, both pairs of base angles are
, and opposite angles are
4. Theorem – Theorem 6-19
If quadrilateral is an isosceles trapezoid, then each pair of base angles is congruent.
.
Geometry
Ms. Gong
Feb.18-Note
5. Investigation –Theorem 6-20
Direction
Isosceles trapezoid FGHK has been plotted on the coordinate plane to the right.
Draw in diagonals ̅̅̅̅
𝐹𝐻 and ̅̅̅̅
𝐺𝐾 , and find their lengths using the distance formula.
F
The distance between 𝐴(𝑥1 , 𝑦1 ),and B(𝑥2 , 𝑦2 )
𝑑 = √(𝑥2 − 𝑥1 )2 + (𝑦2 − 𝑦1 )2
G
FH=
K
H
GK=
Conjecture3:
The diagonals of an isosceles trapezoid are
6. Theorem – Theorem 6-20
If quadrilateral is an isosceles trapezoid, then its diagonals are congruent
7. Summary – Theorem 6-19 to 6-20
Theorem 6-19
If a quadrilateral is an isosceles trapezoid, then each pair of base angles is __________________.
Question1
.
Geometry
Ms. Gong
Feb.18-Note
Theorem 6-20
If a quadrilateral is an isosceles trapezoid, then its diagonals are __________________.
8. Problem2 - Finding angles measures in trapezoids
𝑪𝑫𝑬𝑭 is an isosceles trapezoid and 𝑚∠𝐶 = 65. What are 𝑚∠𝐸, and 𝑚∠𝐹?
9. Problem2 - Finding angles measures in isosceles trapezoids
The second ring of the paper fan shown at the right consists of 20 congruent isosceles trapezoids that
appear to form circles. What are the measures of the base angles of these trapezoids?
Step1: Find the measure of each angle at the center of the fan.
This is the measure of the vertex angle of an isosceles triangle.
Step2: Find the measure of each acute angle base angle of an isosceles triangle.
Step3: Find the measure of each obtuse base angle of the isosceles trapezoid.
Geometry
Ms. Gong
Feb.18-Note
EXERCISE
3. A fan has 15 angles meeting at the center. What are the measures of the base angles of the
congruent isosceles trapezoids in its second ring?
HW: 6.6 Trapezoids and Kites, p.395-397, #7-12, 28-30