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Construct a tree diagram of all the types of quadrilaterals and briefly explain the hierarchical relationships that exist in your tree.

Different textbooks define trapezoid differently. Some define a trapezoid as a quadrilateral with exactly one pair of parallel sides, while others define it as a quadrilateral with at least one pair of parallel sides. How might your tree diagram from Problem change if you were to use the alternative definition of a trapezoid? Draw the revised tree diagram below and explain any changes.

TRUE OR FALSE: Explain each choice.

If the opposite angles of a quadrilateral are congruent, then the quadrilateral must be a rectangle.

If one angle of a rhombus is a right angle, then all the angles of the rhombus are right angles.

If one angle of a trapezoid is a right angle, then the trapezoid must be a rectangle.

If the diagonals of a parallelogram are congruent, then the parallelogram must be a square.

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01:33

The figure shown below is an isosceles trapezoid. The two sides that are not parallel have the same length. How could you add this shape to the family tree diagram?

An isosceles trapezoid is a quadrilateral. All squares are rectangles. All equilateral triangles are equilateral quadrilaterals. All rectangles are parallelograms. All rhombuses are parallelograms. All parallelograms are quadrilaterals. All trapezoids are quadrilaterals.

Rectangle(Square)11-4, write whether each statement is true or false:1. All trapezoids are parallelograms. – False2. Every trapezoid is a rectangle. – False3. Squares are special parallelograms. – True4. All quadrilaterals are squares. – False5. The figure shown below is an isosceles trapezoid. – True6. Why is a parallelogram not a trapezoid? – The sides of a parallelogram are not parallel.

How do you know if a quadrilateral is a trapezoid? The two sides that are not parallel have the same length. How could you add this shape to the family tree …

02:03

Extension: Construct a tree diagram showing the relationships among the following quadrilaterals: trapezoid, parallelogram, rectangle, rhombus, kite, and square. Start with quadrilateral at the top; as you proceed down, each line segment connecting two figures will indicate that the figures below are subsets of the figures above.

07:29

State whether each of the following statements is TRUE or FALSE. The area of every parallelogram constructed on a geoboard is a whole number. If the sides of a parallelogram are whole numbers, its area is a whole number. The area of every square is a whole number. The area of every parallelogram is a whole number. If a parallelogram has an area of 4 and its base is 6, then its height is 2/3. You only need to know the length of one side of a square to find its area. If two rectangles have the same lengths for their sides, they are congruent and have the same area. If two parallelograms have the same lengths for their sides, they are congruent and have the same area. Two triangles that have the same base and height are congruent. Two triangles that have the same base and height have the same area.

01:51

Determine whether the parallelogram none. Explain: is a rhombus, rectangle, square, 0r See Problem 8. P( -1, 2) , 0(0,0), S(4,0), T(3,2) L(L, 2), M(3,3), N5, 2) , P(3,1) 10 . R(-2, -3) , S(4,0), T(3,2), V(-3,-1) 11. G(O, 0) , H(6, 0) , I(9,1), K3,1) 12. W-3,0) , I(0,3), N(3,0), D(O , ~3) 13. S(1,3) , P(4,4), A(3,1), Tlo, 0)What is the most precise classification of the quadrilateral formed by See Problem connecting in order the midpoints of each figure below? 14. parallelogram PART 15. rectangle EFGH 16. isosceles trapezoid JKLM

03:09

Raised quadrilateral garden bed with surrounding design for an unconnected at the edges. The Dikeh Tyler creates his own quadrilateral sections with approximate lengths of the sections with four congruent sides, measured in inches. 10x, 4x, 10x, 3x + 1, 2x + 3, 10x.

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