Describe what a polygon is. Include a discussion about the parts of a polygon. Also compare and contrast a convex with a concave polygon. Compare and contrast equilateral and equiangular. Give 3 examples of each.

 

 POLYGON: A polygon is a 3 or more sided figure. The figures should be closed plane. 

 

Concave polygons: One or more vertices that will point inward or in. While a Convex, is a polygon where ALL vertices point OUT. 

 

Equilateral:                                                                                                     Equilangular 

All 3 sides are congruent! All sides are congruent.                                       The angles are all congruent.

 

                                               They can be compared because all parts are congruent.

 

EXAMPLES: 

 

 

  polygons.

 

 

concave and convex.

 

 

 

 EQUILATERAL

 

 

EQUIANGULAR

 

 

 

 Explain the Interior angles theorem for quadrilaterals. Give at least 3 examples.

 

Interior Angles Theorem: The interior angle theorem states that the sum all the angle measures and equals the sum of the angle measures. We use the formula to do this:   (n-2) 180 = n being number of sides. 180 total sum of angles.

 

Examples: 

 

 

 

 Describe the 4 theorems of parallelograms and their converse and explain how they are used. Give at least 3 examples of each.

 

The 4 theorems of parallelograms are: 

 

1. If a quadrilateral is a parallelogram, then its opposite sides are congruent. 

 

 

 

 

2. If a quadrilateral is a parallelogram, then its opposite angles are congruent.

 

 

 

 

3. If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

 

4. If a quadrilateral is a parallelogram, then its diagonals bisect each other.

 

 

Describe how to prove that a quadrilateral is a parallelogram. Include an explanation about theorem 6.10. Give at least 3 examples of each.

 

A quadrilateral is a parallelogram because it is a figure with 2 pairs of parallel sides. 

 

first because they have parallel sides. 

2) the opposite sides are always congruent. 

3) one pair of sides are congruent and the other is parallel. 

 

6.10= it is the same, they have both congruent angles and congruent sides, that makes them congruent. 

 

EXAMPLES: 

 

 

 

 

Compare and contrast a rhombus with a square with a rectangle. Describe the rhombus, square and rectangle theorems. Give at least 3 examples of each.

 

Rhombus: 

Parallelogram with 4 congruent sides.

It's diagonals are congruent. And are perpendicular. 

 

 

 

Rectangle: 

A parallelogram with a right angles. 

Its diagonals are adjacent. 

 

 

 

Square: 

Quadrilateral with 4 right angles and 4 congruent sides. 

4 sided regular polygon with all sides equal and all angles measuring 90 degrees.

opposite sides are parallel. 

diagonals bisect each other at right triangles. 

diagonals are congruent.

 

 

 

Describe a trapezoid. Explain the trapezoidal theorems. Give at least 3 examples of each.

 

A trapezoid is a quadrilateral with pair of parallel sides. Which are the bases.

 

Isosceles: 

2 non-parallel sides are congruent. (legs)

 

Base angles are congruent.

Diagonals are also congruent.

midsegment length: b1+b2

both sets of angles are congruent.

 

EXAMPLES:

 

 

 

 

 

Describe a kite. Explain the kite theorems. Give at least 3 examples of each.

 

A kite is a quadrilateral with 2 pairs of adjacent congruent sides.

 

It is a quadrilateral.

 

It has 1 pair of congruent opposite angles.

Diagonals are perpendicular, longer diagonal bisects the short one.

 

Theorems: 

If a quadrilateral is a kite, then its diagonals are perpendicular.

If a quadrilateral is a kite, then one pair of opposite angles are congruent. 

 

EXAMPLES: