Geometry Angles of Polygons Properties of Parallelograms Proving Quadrilaterals are Parallelograms Constructing Parallelograms Rhombi, Rectangles and Squares Kites Families of Quadrilaterals Coordinate Proofs Proofs Click on a topic to 1
Polygon is a closed figure made of line segments connected end to end. Since it is made of line segments, Can you explain why the figure below is not a polygon? Convex polygons convex if no line polygon contains a point in the interior of the polygon. interior 2
Concave polygons interior 1 2 3
3 Indentify the polygon. Quadrilateral Hexagon Decagon 4 Is the polygon convex or concave? 5 Is the polygon convex or concave? 4
all its sides are congruent. 6 Describe the polygon. (Choose all that apply) Pentagon Concave Quadrilateral Hexagon Equiangular Regular 7 Describe the polygon. (Choose all that apply) Pentagon Concave Quadrilateral Hexagon Equiangular Regular 5
8 Describe the polygon. (Choose all that apply) Pentagon Concave Quadrilateral Hexagon Equiangular Regular What do you notice about the regions created by the diagonals? click 1(180 6
Given: 180(6-2) = 720 7
-153 387 x = 43 o o o o o +146 o +129 o =540 o o o o polygon is: 9 8
regular 20-gon? 9
(9x-6), is 360 10
polygon with n sides is 11
o to find n. 12
o o Properties of 13
Click on the links below and complete the two labs before the Parallelogram lesson. Lab - Investigating Parallelograms Lab - Properties of Parallelograms Parallelograms is a quadrilateral whose both pairs of opposite sides are parallel. D In parallelogram DEFG, If a quadrilateral is a parallelogram, then its opposite sides are congruent. D C 14
Theorem Q4 If a quadrilateral is a parallelogram, then its opposite angles are congruent. Theorem Q5 = 180 D 5z C 15
D C The consecutive angles are 5z 16
D D 17
D Theorem Q5 If a quadrilateral is a parallelogram, then the diagonals D C 18
sometimes 6 7 8 9 19
6 7 8 9 20
Theorem Q6 D C 21
Theorem Q7 D C 22
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Theorem Q8 D C Theorem Q9 D C Theorem Q10 D C 24
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parallel supplementary 26
parallel supplementary 27
Construct a Parallelogram 28
Construct a Parallelogram - Step 1 Construct a Parallelogram - Step 2 Construct a Parallelogram - Step 3 parallelogram? 29
3 steps t the length of the segment. 3 steps t 3 steps t Step 3 - Connect the endpoints parallelogram? 30
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other. and Squares 32
Rhombus Rhombus Corollary D C rhombus? 33
rhombus? D C Theorem Q12 34
EFGH is a rhombus. EF = HG 2x-6 = 10 = x = 8 are supplementary z = m F z = (108 z = 54 35
This is a rhombus. Find x. This is a rhombus. Find x. This is a rhombus. Find x. 36
HJKL is a rhombus. Find the length of HJ. Rectangle Corollary A, B, C and D are right angles. rectangle? 37
Theorem Q13 D C 63 C 38
Square Corollary a properties of a 39
2 3 4 5 2 3 4 5 40
rhombus Diagonals bisect 41
Click on the link below and complete the lab. Lab - Quadrilaterals in the Coordinate Plane trapezoid is a quadrilateral with base base The parallel sides are called bases. The nonparallel sides are called legs. 42
isosceles trapezoid Theorem Q14 D C Theorem Q15 43
3 5 7 9 3 5 7 9 Theorem Q16 BD. D C 44
The sum of the interior angles of a quadrilateral is 360 9w + 261 = 360 m S = 6w+2 = 6( Option B consecutive interior angles. m P + m S = 180 and m Q + m R = 180 (3w) + 147 = 180 m S = 6w+2 = 6( 45
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No midsegment of a trapezoid Click on the link below and complete the lab. Theorem Q17 EF = (AB+DC) D C 47
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Choose all that apply. 49
kites congruent sides. Click on the link below and complete the lab. Lab - Properties of Kites Theorem Q18 B A C D 50
(Remember M -1) + 48 = 360 = 242 = 121 ± 51
READ is a kite. RE is congruent to. READ is a kite. A is congruent to. 52
Find the value of x. o (3x o o D C 53
Families of Quadrilaterals 54
rhombus parallelogram trapezoid isosceles Description perpendicular rectangle, square of parallel sides Isosceles 55
A rhombus is a square. sometimes A square is a rhombus. sometimes A rectangle is a rhombus. sometimes 56
A trapezoid is isosceles. sometimes sometimes 57
Given: PQRS is a quadrilateral Prove: PQRS is a kite SP = (6-3) PQ = (3-6) 58
RQ = (-2-3) + (-3) = (-5) + (-3) = 25 + 9 = 34 = 5.83 Prove: JKLM is a square K (4,-1) (-3,0) M K (4,-1) We also know that a square is a rectangle and a rhombus. MJ = (3-0) JK = (-1-3) + (4-1) 59
(-3,0) M K (4,-1) 3-0 1-(-3) 4-1-3 MJ JK and MJ JK MJ LK and JK LM (Opposite sides are congruent) JKLM is a square Given: PQRS is a trapezoid 60
Given: TE MA, <1 <2 EM click each pair of opposite sides is parallel and congruent 61
Given: FGHJ is a parallelogram, F is a right angle Prove: FGHJ is a rectangle statements Given: COLD is a quadrilateral, m O=140, m D =40 Prove: COLD is a trapezoid 62
statements Given: FCD Prove: FD CE FED 63