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Honors Geometry Special Quadrilaterals. True/False Every square is a rhombus.

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Presentation on theme: "Honors Geometry Special Quadrilaterals. True/False Every square is a rhombus."— Presentation transcript:

1 Honors Geometry Special Quadrilaterals

2 True/False Every square is a rhombus.

3 TRUE – four congruent sides

4 True/False If the diagonals of a quadrilateral are perpendicular, then it is a rhombus.

5 False – diagonals don’t have to be congruent or bisect each other.

6 True/False The diagonals of a rectangle bisect its angles.

7 FALSE (draw an EXTREME rectangle!)

8 True/False A kite with all consecutive angles congruent must be a square.

9 TRUE

10 True/False Diagonals of trapezoids are congruent.

11 FALSE – not always!

12 True/False A parallelogram with congruent diagonals must be a rectangle.

13 TRUE

14 True/False Some rhombuses are rectangles.

15 True – some rhombuses also have right angles

16 True/False The diagonals of a rhombus are congruent.

17 False – not always!

18 True/False If the diagonals of a parallelogram are perpendicular, it must be a rhombus.

19 TRUE

20 True/False Diagonals of a parallelogram bisect the angles.

21 FALSE

22 True/False A quadrilateral that has diagonals that bisect and are perpendicular must be a square.

23 FALSE (could be rhombus… right angles not guaranteed)

24 Sometimes/Always/Never A kite with congruent diagonals is a square.

25 FALSE – could be, but diagonals don’t have to bisect each other.

26 Give the most descriptive name: A parallelogram with a right angle must be what kind of shape?

27 Rectangle

28 Give the most descriptive name: A rectangle with perpendicular diagonals must be what kind of shape?

29 SQUARE

30 Give the most descriptive name A rhombus with consecutive angles congruent must be a:

31 SQUARE

32 Give the most descriptive name: A parallelogram with diagonals that bisect its angles must be a:

33 Rhombus

34 Proving that a Quad is a Rectangle If a parallelogram contains at least one right angle, then it is a rectangle. If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle. If all four angles of a quadrilateral are right angles, then it is a rectangle.

35 Proving that a Quad is a Kite If two disjoint pairs of consecutive sides of a quadrilateral are congruent, then it is a kite. If one of the diagonals of a quadrilateral is the perpendicular bisector of the other diagonal, then it is a kite.

36 Proving that a Quad is a Rhombus If a parallelogram contains a pair of consecutive sides that are congruent, then it is a rhombus. If either diagonal of a parallelogram bisects two angles of the parallelogram, then it is a rhombus. If the diagonals of a quadrilateral are perpendicular bisectors of each other, then the quadrilateral is a rhombus.

37 Proving that a Quad is a Square If a quadrilateral is both a rectangle and a rhombus, then it is a square.

38 Proving that a Trapezoid is Isosceles If the non-parallel sides of a trapezoid are congruent, then it is isosceles. If the lower or upper base angles of a trapezoid are congruent, then it is isosceles. If the diagonals of a trapezoid are congruent, then it is isosceles.


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