Essential Question: Describe the characteristics of Parallelograms. (Sides and Angles) Unit 5 Lesson 1 Parallelograms

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A parallelogram is Abbreviation:

Opposite Sides Opposite Angles Consecutive Angles Properties that are true for ALL parallelograms    

Opposite sides are parallel Opposite sides are congruent Opposite angles are congruent An angle is supplementary to both its consecutive angles Diagonals bisect each other One pair of opposite sides are congruent and parallel

Example #1: Determine whether each quadrilateral is a parallelogram. Justify your answer. a) b) c)

Example #2: If ABCD is a parallelogram, determine the following:

1. m∠A = ___________

2. m∠D = ___________

3. m∠C = ___________

4. X = ______________

5. CD = ______________

6. AB = _____________

Practice: Find the measures of the numbered angles for each parallelogram.

a)

∠1 = _________ ∠2 = _________ ∠3 = _________

b)

c)

∠1 = _________ ∠2 = _________ ∠3 = _________

∠1 = _________ ∠2 = _________ ∠3 = _________

Example #3: Find the coordinates of the intersection of the diagonals of HJKL with the given vertices. H(2,3) J(1, –2) K(–5, –7) and L(–4, –2)

Example #4: Find the value of each variable in the following parallograms: a) b) c)

Example #5: Find the value of each variable so that each quadrilateral is a parallelogram. a) b) c)

Essential Question: Describe the characteristics of Rectangles. (Angles, Sides, and Diagonals) Unit 5 Lesson 2 Rectangles Rhombi, and Squares

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Rectangle

Rhombus

Square

Example #1: Quadrilateral QRST is a rectangle. Find the value of x and then calculate the length of each diagonal. a) QS = 4x – 7 and RT = 2x + 11

b) TR = 4x – 45 and SQ = x + 45

Example #2: Graph each quadrilateral with the given vertices. Determine whether the figure is a rectangle. Justify your answer using the indicated formula. a) A(4,1) B(–3,2) C(3, –1) and D(–2,4)

b) X(–2,4) G(1, –2) H(–1, –3) and Y(–4,3)

Distance Formula

Slope Formula

Example #3A: Quadrilateral ABCD is a rectangle. Answer the following questions: a) If AC = 2x + 13 and DB = 4x –1, then x = ______ and DB = ______.

b) If m∠DAC = 2x + 4 and m∠BAC = 3x + 1, then x = _______ and ∠BAC = _______.

Example #3B: Quadrilateral DKLM is a rhombus. Answer the following questions: a) If DK = 8, then KL = _______. b) If m∠KAL = 2x – 8, then x = _______.

c) If DA = 4x and AL = 5x – 3, then x = ______ and AD = ______.

Example #4: What are the measures of the numbered angles in the rhombi? a)

∠1 = _________ ∠2 = _________ ∠3 = _________ ∠4 = _________

b)

c)

∠1 = _________ ∠2 = _________ ∠3 = _________ ∠4 = _________

∠1 = _________ ∠2 = _________ ∠3 = _________

Example #5: For what value of x and/or y is the parallelogram ABCD a rhombus? a)

b)

Essential Question: Describe the characteristics of rhombi and squares. Compare and Contrast.

Unit 5 Lesson 3 Comparing Rectangles, Rhombi, and Squares

________________________________________________________________________________ ________________________________________________________________________________ ________________________________________________________________________________ ________________________________________________________________________________ Example #1: Determine if each figure is a rhombus, rectangle, or square. EXPLAIN WHY. a)

b)

c)

d)

e)

f)

Example #2: For what value of x or y is the figure given a special parallelogram? a) Square

b) Rhombus

c) Rectangle

d) Rectangle

e) Rhombus

f) Rectangle

Example #3: Name all of the special parallelograms that have each property: A.) Diagonals are perpendicular – B.) Diagonals are congruent – C.) Diagonals are angle bisectors – D.) Diagonals bisect each other – E.) Diagonals are perpendicular bisectors of each other –

Example #4: Given each set of vertices, determine whether QRST or BEFG is a rhombus, rectangle, or square. List all that apply. a)

b)

c)

Essential Question: Describe the characteristics of Trapezoids and Kites. Compare and Contrast.

Unit 5 Lesson 4 Trapezoids and Kites

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Properties

Illustration

Example #1: CDEF is an isosceles trapezoid and m∠C = 65. What are m∠D, m∠𝐸, and m∠F?

Example #2: All of the trapezoids are isosceles trapezoids. Find the missing angle

measures. 1.

2.

∠𝑄 = _________ ∠𝑃 = _________ ∠𝑆 = _________

∠1 = _________ ∠2 = _________ ∠3 = _________

3.

∠1 = _________ ∠2 = _________ ∠3 = _________

4.

∠1 = _________ ∠2 = _________ ∠3 = _________

Example #3: QR is the midsegment of trapezoid LMNP. What is x? What is QR?

Your Turn: EF is the midsegment of trapezoid ABCD. Calculate the value of x and the length of the midsegment. a)

b)

Shape and Definition

Properties

Illustration

Example #4: Find the measure of the numbered angles in the kites below:

1.

2.

∠1 = _______ ∠2 = _______ ∠3 = _______

∠1 = _______ ∠2 = _______ ∠3 = _______

3.

∠1 = ____ ∠4 = ____ ∠2 = ____ ∠5 = ____ ∠3 = ____

Example #5: Find the values of the variables in each kite. a)

b)

4.

∠1 = ____ ∠4 = ____ ∠2 = ____ ∠5 = ____ ∠3 = ____

Unit 6 Lesson 5

Essential Question: What can you use to classify polygons in the coordinate plane?

Coordinate

Geometry

Example #1: A(

,

)

Length of AB

Your Turn:

B(

,

) Length of BC

C(

,

) Length of AC

In order to be a rhombus, what MUST be true?

Example #2: A(

,

)

B(

,

)

C(

,

)

D(

,

)

Your Turn:

Your Turn:

Graph and label each quadrilateral with the given vertices. Then determine the most precise name for each quadrilateral.

Section 6.8

Your Turn: