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 Polygon Quadrilateral Triangle
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 Add the following figures to the hierarchy tree: Pentagon
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.