Lesson 1
![Picture](/uploads/3/8/6/0/38601155/7739727.jpg?300)
In this lesson we will be talking about polygons and their different properties.
Polygon- A 2-dimensional figure with three or more straight lines and angles. They are enclosed meaning there aren't any openings and all the lines are connected.
Types of Polygons:
Polygon- A 2-dimensional figure with three or more straight lines and angles. They are enclosed meaning there aren't any openings and all the lines are connected.
Types of Polygons:
- Convex Polygon- Is defined as a polygon where the points of the diagonal don't lie beyond the interior
- Concave Polygon- A polygon where the points of a diagonal lie on the exterior which causes at least one angle to be greater than 180 degrees.
![Picture](/uploads/3/8/6/0/38601155/8406961.jpg?545)
Common polygons:
- Triangle-3 sided polygon
- Quadrilateral-4 sided polygon
- Pentagon- 5 sided polygon
- Hexagon-6 sided polygon
- Heptagon-7 sided polygon
- Octagon-8 sided polygon
- Nonagon-9 sided polygon
- Decagon-10 sided polygon
Interior Angles of a regular Polygon:
Exterior Angles of a regular polygon:
- Each polygon has a different sum of interior angles
- You can use the formula (n-2)180 to find the sum of the interior angles of a polygon
- To find each individual angle of a regular polygon you use (n-2)180/n.
Exterior Angles of a regular polygon:
- Each polygon has the same sum of exterior angles
- That sum is 360 degrees
- To find each individual exterior angle of a regular polygon you divide 360 by the number of sides
Lesson 2 and Lesson 3
In this lesson we'll be talking about the properties of parallelograms and how to prove that a quadrilateral is a parallelogram.
Theorem 1- If opposite sides are parallel and then it's a parallelogram
Theorem 2- If opposite sides are congruent then it's a parallelogram
Theorem 3- If opposite angles are congruent then it's a parallelogram
Theorem 4-If the diagonals bisect each other then it is a parallelogram.
Theorem 5-If one set of sides are parallel and congruent then it is a parallelogram.
Theorem 6-If the consecutive angles are supplementary then it is a parallelogram.
All these properties pass down to different types of Parallelograms.
The parallelogram passes down traits to rectangles. rhombuses, and squares as you can see below
Theorem 1- If opposite sides are parallel and then it's a parallelogram
Theorem 2- If opposite sides are congruent then it's a parallelogram
Theorem 3- If opposite angles are congruent then it's a parallelogram
Theorem 4-If the diagonals bisect each other then it is a parallelogram.
Theorem 5-If one set of sides are parallel and congruent then it is a parallelogram.
Theorem 6-If the consecutive angles are supplementary then it is a parallelogram.
All these properties pass down to different types of Parallelograms.
The parallelogram passes down traits to rectangles. rhombuses, and squares as you can see below
Lesson 4
![Picture](/uploads/3/8/6/0/38601155/7508839.png?193)
In this lesson we'll talk about the different types of parallelograms.
Rectangle- A quadrilateral that has only right angles.
-Properties- All the same properties of a parallelogram,diagonals are congruent,contains four right angles
-Theorems-If a diagonals are congruent then it is a parallelogram,If it has four right angles then it is a rectangle
Rectangle- A quadrilateral that has only right angles.
-Properties- All the same properties of a parallelogram,diagonals are congruent,contains four right angles
-Theorems-If a diagonals are congruent then it is a parallelogram,If it has four right angles then it is a rectangle
![Picture](/uploads/3/8/6/0/38601155/4255475.png?206)
Rhombus- A parallelogram with side that are all congruent
-Properties- All the same properties as a parallelogram, all sides are equal, the diagonals are perpendicular bisectors, diagonals bisect opposite angles
-Theorems- If it has 4 congruent sides then it is a rhombus, If the diagonals are perpendicular bisectors then it is a rhombus, If a diagonal bisects a pair of opposite angles then it is a rhombus.
-Properties- All the same properties as a parallelogram, all sides are equal, the diagonals are perpendicular bisectors, diagonals bisect opposite angles
-Theorems- If it has 4 congruent sides then it is a rhombus, If the diagonals are perpendicular bisectors then it is a rhombus, If a diagonal bisects a pair of opposite angles then it is a rhombus.
![Picture](/uploads/3/8/6/0/38601155/7664977_orig.png)
Square- A combination of a rhombus and rectangle, containing 4 right angles and all the sides are congruent.
-Properties- The combination of the properties of a rectangle and a rhombus.
-Theorems- If it is a rectangle and a rhombus then it is a square.
You can use this information to prove something is one of these shapes.
Note: In the quadrilateral family tree you always back track, for example a square can be a rectangle, but a rectangle isn't always a square.
-Properties- The combination of the properties of a rectangle and a rhombus.
-Theorems- If it is a rectangle and a rhombus then it is a square.
You can use this information to prove something is one of these shapes.
Note: In the quadrilateral family tree you always back track, for example a square can be a rectangle, but a rectangle isn't always a square.
Lesson 5
![Picture](/uploads/3/8/6/0/38601155/3298044.png?244)
In this lesson we will learn about the rest of the quadrilaterals, trapezoid and kite.
Trapezoid- a quadrilateral with exactly one pair of parallel sides.
Properties of isosceles trapezoid- legs are congruent, base angles are congruent, diagonals are congruent
Midsegment theorem- the midsegment is parallel to the base sides and it's length is found by averaging the two bases
Trapezoid- a quadrilateral with exactly one pair of parallel sides.
Properties of isosceles trapezoid- legs are congruent, base angles are congruent, diagonals are congruent
Midsegment theorem- the midsegment is parallel to the base sides and it's length is found by averaging the two bases
![Picture](/uploads/3/8/6/0/38601155/6005599_orig.jpg)
Kite- a quadrilateral with exactly two pairs of congruent consecutive sides.
Properties- They have exactly one pair of opposite angles that are congruent, the diagonals are perpendicular bisectors
Theorems- If a quadrilateral is a kite, then its diagonals are perpendicular, if a quadrilateral is a kite, then exactly one pair of opposite angles is congruent.
Properties- They have exactly one pair of opposite angles that are congruent, the diagonals are perpendicular bisectors
Theorems- If a quadrilateral is a kite, then its diagonals are perpendicular, if a quadrilateral is a kite, then exactly one pair of opposite angles is congruent.
Lesson 7
In this lesson we will discuss the different formulas used to find areas of certain shapes
All these formulas can be used to find the areas of abnormal shapes like the one beloew:
- A parallelogram's area can be found, when given base and height, by using the formula A=bh
- A square's area can be found by the formula s squared.
- The area of a rhombus or the area of a kite can be figured out by using the formula A=1/2*d1*d2
- The area of a trapezoid can be found by using the formula A=1/2*h(b1+b2)
- The area of a triangle can be found by using A=1/2*bh
- You can uae pi*r squared to find the area of circle
All these formulas can be used to find the areas of abnormal shapes like the one beloew:
Lesson 8
In this lesson we will talk about finding the area of regular polygons
To find the area of a regular polygon you need to know the formula A=1/2aP. This formula is useful when you aren't able to use any of the other given formulas.
Useful Terms:
If you aren't given the apothem, you could use the radius to help find it and vise versa.
To find the area of a regular polygon you need to know the formula A=1/2aP. This formula is useful when you aren't able to use any of the other given formulas.
Useful Terms:
- The radius of a regular polygon is the distance from the center to the vertex.
- The apothem of a regular polygon is the perpendicular distance from the center to a side.
If you aren't given the apothem, you could use the radius to help find it and vise versa.
Lesson 9
In this lesson we will talk about scale factors and the relationships between similar figures.
It is often assumed that the ratio between the sides, perimeters, and areas of similar figures are the same. The ratio between perimeters and the ratio between side lengths are the same, but it is not like that with the area.
Ratio of side lengths- a:b
Ratio of perimeters- a:b
Ratio of areas- a squared:b squared
It is often assumed that the ratio between the sides, perimeters, and areas of similar figures are the same. The ratio between perimeters and the ratio between side lengths are the same, but it is not like that with the area.
Ratio of side lengths- a:b
Ratio of perimeters- a:b
Ratio of areas- a squared:b squared