I am working on a geometry problem where I have to build a mobile of the quad. family. I have to state the properties of each figure. For a parallelogram I have 1. opp. sides are congruent 2. opp. angles are congruent 3. diagonals bisect each other and are congruent. For a rhombus I have 1. each diagonal bisects and are perpendicular. For a trapezoid I have the midsegment half the length of the base.
I have nothing for a rectangle, square, kite or isosceles trapezoid.
My question is are the ones I have correct and can you help me with the properties I don't have
For a parallelogram, add:
- opposites sides are parallel
For a rhombus, add:
all the properties of a parallelogram, plus
- diagonals are angle bisectors
- ______ axes of symmetry
For a trapezoid, add:
- ____ pair of parallel opposite sides
For a rectangle, add:
all the properties of a parallelogram, plus
- _________ sides are perpendicular to each other
- ___ axes of symmetry
For a square, add:
all the properties of a rectangle, plu
- all sides are congruent
- ____ axes of symmetry
For a kite:
- has ____ pairs of congruent adjacent sides.
- Diagonals are perpendicular to each other
- ____ of the diagonals is an axis of symmetry, therefore it bisects the internal angles.
For an isoceles trapezoid,
- _____ pair of opposite parallel sides
- _____ axis of symmetry
Yes, the properties you have stated for a parallelogram and a rhombus are correct. However, there are additional properties for a parallelogram and a rhombus that you could include.
For a parallelogram:
1. Opposite sides are congruent
2. Opposite angles are congruent
3. Diagonals bisect each other and are congruent
Additional properties:
4. Consecutive angles are supplementary (sum to 180 degrees)
5. Opposite sides are parallel
For a rhombus:
1. Each diagonal bisects the opposite angles and is perpendicular
Additional properties:
2. Opposite sides are congruent
3. All angles are congruent (each angle measures 90 degrees)
4. Diagonals are perpendicular bisectors of each other
Now, let's discuss the properties for a rectangle, square, kite, and isosceles trapezoid.
Rectangle:
1. Opposite sides are congruent
2. Opposite angles are congruent
3. Diagonals are congruent and bisect each other
Additional properties:
4. Each angle measures 90 degrees (rectangle is a special case of a parallelogram where all angles are right angles)
5. All sides are congruent (since opposite sides are congruent in a rectangle)
Square:
1. Each side is congruent
2. All angles are congruent (each angle measures 90 degrees)
3. Diagonals are congruent and bisect each other
Additional properties:
4. Opposite sides are parallel and congruent (since square is a special case of a parallelogram and a rectangle)
Kite:
1. Adjacent sides are congruent
2. Diagonals are perpendicular
Additional properties:
3. One pair of opposite angles is congruent
4. One diagonal bisects the other diagonal
Isosceles Trapezoid:
1. Exactly one pair of opposite sides is parallel
2. Legs (non-parallel sides) are congruent
3. Base angles (angles formed by the legs and the base) are congruent
Additional properties:
4. Diagonals are congruent
5. Median (midsegment) is parallel to the bases and half the length of the sum of the bases
I hope this helps you with your geometry problem! Let me know if you have any further questions.