Notes: Find Angle Measures in Polygons 8.1

Objective: Find angle measures in polygons

Find the sum of the measures of the interior angles of the indicated convex polygon.

1) Nonagon 2) 16 – gon

The sum of the measures of the interior angles of a convex polygon is given. Classify the

polygon by the number of sides.

3) 360 4) 1980

Find the value of x.

5) 6)

Notes: Find Angle Measures in Polygons 8.1

Find the value of x.

7) 8)

Find the measures of an interior angle and an exterior angle of the indicated regular

polygon.

9) regular pentagon 10) regular 90-gon

Find the value of n for each regular n-gon described.

11) Each exterior angle of the regular n-gon has a measure of 9 .

Notes: Use Properties of Parallelograms 8.2 Objective: Find angle and side measures in parallelograms

Find the value of each variable in the parallelogram.

1) 2)

3) 4)

Notes: Use Properties of Parallelograms 8.2 Find the measure of the indicated angle in the parallelogram.

5) Find Bm 6) Find Ym

7) In ABCD, Cm is 20 degrees more than Dm . Sketch ABCD. Find the measure of

each interior angle. Then label each angle with its measure.

Find the value of each variable in the parallelogram.

8) 9)

Find the indicated measure in ABCD. Explain your reasoning.

10) AEBm 11) ACBm

12) DBCm 13) CABm

14) DCBm 15) ADCm

16) The measure of one interior angle of a parallelogram is 20 degrees more than 3 times the

measure of another angle. Find the measure of each angle.

Notes: Show that a Quadrilateral is a Parallelogram 8.3

Objective: Use properties to identify parallelograms

1) The figure shows part of a stair railing. Explain how you know the support bars MP and NQ

are parallel.

2) In quadrilateral WXYZ, 42 , 138 , 42 .m W m X m Y Find m Z . Is WXYZ a

parallelogram? Explain your reasoning.

Notes: Show that a Quadrilateral is a Parallelogram 8.3

For what value of x is the quadrilateral a parallelogram?

3) 4) 5)

6) The vertices of quadrilateral ABCD are given. Draw ABCD in a coordinate plane and

show that it is a parallelogram.

( 2, 3), (0,5), (6,5), (4, 3)A B C D

7) Three of the vertices of ABCD are given. Find the coordinates of point D.

( 3,4), (4,6), (3, 1), ( , )A B C D x y

*Use graph paper for #12, 14, 26, 28 in homework 8.3

Notes: Properties of Rhombuses, Rectangles, and Squares 8.4

Objective: Use properties of rhombuses, rectangles and squares

Parallelogram

Opposite sides are parallel

Rectangle Rhombus

Opposite sides are parallel Opposite sides are parallel

Four right angles Four congruent sides

Square

Opposite sides are parallel

Four right angles

Four congruent sides

Diagonals of a Rhombus: Diagonals of a Rectangle:

Diagonals are perpendicular Diagonals are congruent Diagonals bisect the opposite angles

**All 3 properties apply to a SQUARE since a square is a ____________ and a ______________

** We also know that the diagonals ____________ each other on ALL parallelograms

Notes: Properties of Rhombuses, Rectangles, and Squares 8.4

For any rhombus QRST, decide whether the statement is always, or sometimes true.

Draw a sketch and explain your reasoning.

1) SQ 2) RQ 3) RSQR 4) RTQS

For any rectangle ABCD, decide whether the statement is always or sometimes true.

Draw a sketch and explain your reasoning.

5) CDAB 6) BCAB 7) CBDABD 8) BDAC

Name each quadrilateral – parallelogram, rectangle. rhombus, and square – for which the

statement is true.

9) It is equiangular 10) Opposite sides are parallel 11) Diagonals bisect each other

Classify the special quadrilateral. Then solve for the variables.

12)

The diagonals of rhombus QRSP intersect at T. Given that 30SPTm and RT = 6, find the

indicated measure.

13) QPRm 14) QTRm 15) PSRm

The diagonals of rectangle WXYZ intersect at P. Given that 50YXZm and XZ = 12, find the

indicated measure.

16) XZYm 17) WPXm 18) ZP

Notes: Use Properties of Trapezoids and Kites 8.5

Objective: Use properties of trapezoids and kites

Points A, B, C, and D are vertices of a quadrilateral. Determine whether ABCD is a trapezoid.

1) )1,2(),2,8(),4,4(),4,0( DCBA 2) )4,1(),3,3(),1,6(),1,2( DCBA

3) Find .,, MmandLmJm 4) Find .,, HmandGmFm

Notes: Use Properties of Trapezoids and Kites 8.5

Find the length of the midsegment. Find the value of x.

5) 6) 7)

JKLM is a kite. Find Km . Find the side lengths of the kite.

Give answers in simplest radical form.

8) 9) 10)

Notes: Identify Special Quadrilaterals 8.6

Objective: Identify special quadrilaterals

Put an X in the box if the shape ALWAYS has the given property.

Give the most specific name for the quadrilateral. Explain your reasoning.

12) 13) 14)

Notes: Identify Special Quadrilaterals 8.6

Tell whether enough information is given in the diagram to classify the quadrilateral by the

indicated name. Explain.

15) Isosceles Trapezoid 16) Square 17) Rhombus

Which pairs of segments or angles must be congruent so that you can prove that FGHJ is

the indicated quadrilateral? Explain.

18) Kite 19) Isosceles Trapezoid