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Geometry Practice: Angles, Polygons, and Quadrilaterals

This daily check includes finding the sum of interior angles, determining the number of sides in a polygon, and solving angle measurements in parallelograms. It also covers the properties of rhombuses, rectangles, and squares.

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Geometry Practice: Angles, Polygons, and Quadrilaterals

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  1. Daily Check (2 pts each) • Find the sum of the interior angles of a regular convex decagon. • Find the number of sides of a regular convex polygon if the sum of the interior angles is 2520°. • Find the measure of each interior angle of a regular octagon.

  2. Warm up • In Parallelogram ABRN, mA = 3x + 15 and mR = 5x –17. What is the value of x? • In Parallelogram ABRN what is mN? x = 16 mN = 117

  3. EOCT Practice This diagram shows how Pam used a compass and a straightedge to construct K, a point of concurrency for right triangle WKS. What point of concurrency did Pam construct? A centroid B circumcenter C incenter D orthocenter D

  4. EOCT Practice Use this diagram to answer the question. What is the measure of angle QPR? A 15° B 60° C 120° D 175° B

  5. EOCT Practice Question of the Day

  6. Homework Review • Page 306 • 116° 2) 48° 3) 96° 4) a=9, b=11 • 5) x=2, y = 17 6) x=4, y=116 • 7) f=78, g=3.5 8) m=4, n=5 9) j=4.5,k=2 • Page 313 • Cons. Angles Supp. 2) Pair Opp. Sides = • 3) Diagonals Bisect 4) One Pair Parallel and = • 5) 6 6) 8 • 7) 1 8) 79 • 9) 20 10) 31

  7. Math IDay 40 (3-15-11) UNIT QUESTION: What are the properties and characteristics of polygons? Standard: MM1G1.e. Today’s Question: What special properties apply to rhombuses, rectangles, and squares? Standard: MM1G.1.e.

  8. Quadrilaterals Activity

  9. RHOMBI SQUARES RECTANGLES

  10. Rhombus Have all the properties of parallelograms and THREE special properties

  11. RHOMBUS FOUR CONGRUENT SIDES

  12. A quadrilateral is a RHOMBUS if and only if it has four congruent sides

  13. RHOMBUS Diagonals Bisect A Pair of Opposite Angles

  14. RHOMBUS Diagonals are Perpendicular

  15. Rectangle Have all the properties of parallelograms and TWO special properties

  16. RECTANGLE FOUR RIGHT ANGLES

  17. A quadrilateral is a RECTANGLE if and only if it has four right angles

  18. RECTANGLE Diagonals are Congruent

  19. SQUARE FOUR RIGHT ANGLES AND FOUR CONGRUENT SIDES

  20. Square Have all the properties of parallelograms, all the properties of rhombi, and all the properties of rectangles

  21. Let's make a Venn Diagram Relating all of the Properities of our quadrilaterals

  22. QUADRILATERALS RHOMBUSES RECTANGLES Squares PARALLELOGRAMS

  23. QUADRILATERALS 1. Polygon 2. 4 sides 1. Opposite Sides are congruent RHOMBI 1. Diagonals bisect angles RECTANGLES 2. Diagonals perp Squares 1. 4 rt. angles 3. 4 equal sides 2. Diagonals congruent 2. Opposite Angles are congruent 3. Diagonals Bisect 4. Consecutive angles are supplementary PARALLELOGRAMS

  24. PQRS is a rhombus P Q S R

  25. PQRS is a rhombus P Q S R

  26. PQRS is a rectangle

  27. Workbook p. 332 #11 – 24

  28. Homework p. 319 #7-28, not #20 or 24

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