Understanding Hierarchy Diagrams

1. Understanding Hierarchy Diagrams Alignment Lesson Day 46

2. Polygon Review As you review the next several slides, look at the pictorial representations of the polygon. Give all the attributes you can think of about the polygon!

3. Vocabulary Review • Square - a parallelogram with all sides the same length and all right angles • Diagonals are congruent • Diagonals are perpendicular • A quadrilateral

4. Vocabulary Review • Rectangle - a parallelogram with all right angles • Diagonals are congruent • Opposite sides are congruent

5. Vocabulary Review • Rhombus - a parallelogram with all sides the same length • Diagonals are NOT congruent • Diagonals are perpendicular

6. Vocabulary Review • Parallelogram - a polygon with two pairs of parallel sides • A rectangle is a parallelogram • A rhombus is a parallelogram • A square is a parallelogram

7. Vocabulary Review • Trapezoid – a quadrilateral with ONLY one pair of parallel sides • Right trapezoid - a trapezoid with right angles

8. Vocabulary Review • Kite - A quadrilateral with two distinct pairs of congruent, adjacent sides and diagonals that intersect at a right angle.

9. Polygons Vocabulary • Acute Triangle– A triangle that contains only angles less than 90 • All acute angles

10. Polygons Vocabulary • Right Triangle – A triangle that contains one 90º right angle • One right angle • Check right angle using the corner of your piece of paper 90° angle

11. Polygon Vocabulary • Obtuse Triangle- A triangle that contains one angle greater than 90° • One obtuse angle

12. Polygon Vocabulary • Scalene Triangle–A triangle that has sides of all different lengths • All angles have different measures too!

13. Polygon Vocabulary • Isosceles Triangle – A triangle that has two sides the same length • Two of the angles have the same measures too!

14. Polygon Vocabulary • Equilateral Triangle- A triangle that has all sides the same length • All the angles have the same measures too!

15. Hierarchy Tree You may also follow along using the blackline master Day 46 “Hierarchy Tree” Polygon Quadrilateral Triangle Rectangle Rhombus • What do you notice about the shapes as you move down the tree? • The definitions become narrower the lower you move; the definitions of the shapes at the top are broader.

16. Hierarchy Tree Polygon Quadrilateral Triangle Rectangle Rhombus • Why is there an arrow pointing from quadrilateral to rectangle? • A rectangle is a more specific quadrilateral. • Why is there an arrow pointing from quadrilateral to rhombus? • A rhombus is a more specific quadrilateral.

17. Hierarchy Tree Polygon Quadrilateral Triangle Rectangle Rhombus Acute Triangle • Where on the tree would you add acute triangle? • Under triangle. • What attributes of these figures have been used to create this hierarchy diagram? • Number of sides, lengths of sides, number and types of angles.

18. Polygon Quadrilateral Triangle Rectangle Rhombus Acute Triangle Add the following figures to the hierarchy tree: • Pentagon • Square • Obtuse triangle • Right triangle

19. Math Talk….Let’s Discuss where you decided to place the polygons on the hierarchy tree.

20. Find Day 46, “Hierarchy Diagram” Place the following polygons in the “Hierarchy Diagram” Triangle Quadrilateral Acute Triangle Rectangle Pentagon Obtuse Triangle Right Triangle Square Rhombus

21. Practice…. • With a partner, you are to… • Create a different hierarchy tree • Must include at least 10 different polygons • It may include some of the same figures as the hierarchy tree discussed earlier today, but it must include some different ones as well. • Think about classifying figures based on different sets of attributes (symmetry, sets of parallel sides, types of angles) • You will need a copy of your hierarchy tree to complete your homework.

22. Homework • Using your hierarchy tree you created with a partner, create a hierarchy diagram that shows the relationships among shapes. Remember not to compare diagrams or share your thinking with your partner until you are instructed to do so during class tomorrow.