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6-1: Polygon Angle-Sum Theorem

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Presentation on theme: "6-1: Polygon Angle-Sum Theorem"— Presentation transcript:

1 6-1: Polygon Angle-Sum Theorem

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3 What are the measures of a...
… Heptagon? … 17-gon?

4 What is the measure of one interior angle of a regular...
… Hexagon? … Nonagon?

5 What is the measure of angle Y?

6 What is the measure of one exterior angle in...
… a Nonagon? … an Octagon?

7 6-2: Properties of Parallelograms

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10 What is the measure of angle P in the parallelogram?

11 Statements Reasons 1) 2) 3) 4) 5) 1) 2) 3) 4) 5)

12 What are the values of x and y in the parallelogram? What are PR and SQ?

13 6-3: Proving That a Quadrilateral Is a Parallelogram

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18 For what values of x and y must the figures be a parallelogram?

19 Are the quadrilaterals parallelograms?

20 6-4: Properties of Rhombuses, Rectangles, and Squares

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24 Is parallelogram ABCD a rhombus, a rectangle, or a square
Is parallelogram ABCD a rhombus, a rectangle, or a square? What about parallelogram EFGH?

25 What are the measures of the numbered angles in the rhombus?

26 In the rectangle RSBF, SF = 2x + 15 and RB = 5x – 12
In the rectangle RSBF, SF = 2x + 15 and RB = 5x – 12. What is the length of a diagonal?

27 6-5: Conditions for Rhombuses, Rectangles, and Squares

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30 Can you conclude that the diagram is a rhombus, a rectangle, or a square? a Square?

31 For what value of x is ABCD a rhombus
For what value of x is ABCD a rhombus?                   For what value of y is DEFG a rectangle?

32 6-6: Trapezoids and Kites

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36 CDEF is an isosceles trapezoid and the measure of angle C is 65
CDEF is an isosceles trapezoid and the measure of angle C is 65. What are the measures of angles D, E, and F?

37 QR is the midsegment of trapezoid LMNP. What is x?

38 Quadrilateral DEFG is a kite
Quadrilateral DEFG is a kite. What are the measures of angles 1, 2, and 3?

39 6-7: Polygons in the Coordinate Plane

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41 Is ΔABC Scalene, Isosceles, or Equilateral?

42 Is Quadrilateral ABCD a Rhombus?

43 Quadrilateral KITE is a Kite
Quadrilateral KITE is a Kite. What is the most precise classification of the quadrilateral formed by connecting the midpoints of the sides of the kite?

44 6-8: Applying Coordinate Geometry

45 What are the coordinates of the figure?
SQRE is a square where SQ = 2a. The axes bisect each side.  TRI is an isosceles triangle where TI = 2a. The y-axis is the median.

46 What are the coordinates of D, the intersection of the two diagonals of the parallelogram?

47 6-9: Proofs Using Coordinate Geometry

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