Post on 23-Jan-2016
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