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)
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Notes: Find Angle Measures in Polygons 8...Notes: Find Angle Measures in Polygons 8.1 Objective: Find angle measures in polygons Find the sum of the measures of the interior angles
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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.