TODAY IN GOEMETRY…

Warm up: White Board Review 8.1-8.4

Learning Target : 8.5 Use properties of Trapezoids and Kites to determine if a quadrilateral is a Trapezoid or Kite

Independent Practice

Ch.7 Retakes

CH.8 TEST - NEXT WEEK!

WARM UP: Find the value of x.

1. 2.

20 sides = 20-gon

120 °𝑥 °

97 °130 °

150 °8 𝑥 °

5 𝑥 °

5 𝑥 °

WARM UP: Find the value of each variable for the parallelograms.

3. 4.

WARM UP: Classify each of the polygons. Then find the missing variables.

5. 6.

RHOMBUS

RECTANGLE

TRAPEZOID: A quadrilateral with exactly one pair of parallel sides. The parallel sides are called the bases.

𝑋 𝑌

𝑍𝑊

BASE

BASE

LEGLEG

EXAMPLE: Determine whether is a trapezoid.

Slopes of are obviously not parallel. Check the other two segments.

Prove that one pair of opposites sides are parallel:

Slope

Slope

YES! It is a trapezoid!

𝐴𝐵

𝐶𝐷

PRACTICE: Determine whether is a trapezoid.

Slopes of are obviously not parallel. Check the other two segments.

Prove that one pair of opposites sides are parallel:

Slope

Slope

Only one pair of opposite sides are parallel, so this must be a trapezoid.

𝐴𝐵

𝐶

𝐷

ISOSCELES TRAPEZOID: • legs of a trapezoid are

congruent• Each pair of base angles are

congruent.• Diagonals are congruent.

𝑋 𝑌

𝑍𝑊

BASE

BASE

LEGLEG

EXAMPLE: Find .

therefore this quadrilateral is an isosceles trapezoid.

Isosceles trapezoids have congruent base angles:

and is a transversal, therefore and are consecutive interior angles:

Isosceles trapezoids have congruent base angles:

𝒎∠𝑲=𝒎∠ 𝑳=𝟓𝟎°

50 °

𝒎∠ 𝑱=𝒎∠𝑴=𝟏𝟑𝟎°

130 °130 °

PRACTICE: Find .

therefore this quadrilateral is an isosceles trapezoid.

Isosceles trapezoids have congruent base angles:

and is a transversal, therefore and are consecutive interior angles:

Isosceles trapezoids have congruent base angles:

𝒎∠𝑲=𝒎∠ 𝑳=𝟕𝟎°

70 °

𝒎∠ 𝑱=𝒎∠𝑴=𝟏𝟏𝟎°

110°70 °𝐽

𝐾

𝐿𝑀110°

MIDSEGMENT THEOREM FOR TRAPEZOIDS:

𝑏𝑎𝑠𝑒1𝑌

𝑍𝑊

𝐴 𝐵

is the midsegment of trapezoid .

SO…

𝑋

𝑏𝑎𝑠𝑒 2

PRACTICE: Find the value of x.

(𝟐𝟑 )(𝟐𝟑 )

KITE: • Has two pairs of consecutive

congruent sides. • Opposite sides are not

congruent.• Diagonals are perpendicular.• Exactly ONE pair of opposite

angles are congruent.

EXAMPLE: Find the side lengths of the kite, write the lengths in the simplest radical form.

We know that the diagonals in a kite are perpendicular.

Use the Pythagorean theorem to find :

Use the Pythagorean theorem to find :

√ 461

√ 461 5√5

5√5

PRACTICE: Find the side lengths of the kite, write the lengths in the simplest radical form.

We know that the diagonals in a kite are perpendicular.

Use the Pythagorean theorem to find :

Use the Pythagorean theorem to find :

√ 41

√ 41

4√10

4√10𝑊

𝑋

𝑌

𝑍

45412

EXAMPLE: is a kite. Find .

𝑊

𝑋

𝑌

𝑍

40 ° 30 °𝑥 °

𝑥 °

and have to be congruent.

EXAMPLE: is a kite. Find .

𝑊

𝑋

𝑌

𝑍

20 °

𝑥 °

𝑥 °

and have to be congruent.

HOMEWORK #5:

Pg. 546: 3-16, 18-23

If finished, work on other assignments:

HW #1: Pg. 510: 3-16, 19, 24-26HW #2: Pg. 518: 3-11, 13-15, 23-31HW #3: Pg. 526: 8-14, 19-21, 25-27, 43-47HW #4: Pg. 537: 3, 14, 19-25