Unit 5 Notes - By: Christina Cui
Lesson 1: In this lesson we learned how to classify polygons and find the interior/exterior angles of one. One of the most important things you need to know in this lesson is the angle sum theorem(n-2)180degrees. It'll prove to be very useful in finding the interior angles of a convex polygon, where there is no diagonals that contain the exterior angles within the polygon itself. Another important thing to know is that the exterior angles of the polygon will most likely ALWAYS equal 360 degrees. To find the measure of the exterior angle of a regular polygon, just divide 360degrees by however many sides the polygon has.
Lesson 2 and 3: No parallelograms aren't parallel gram crackers. Let's get a basic understand of what a parallelogram is and what will make something a parallelogram. There are four simple theorems. 1. Parallelogram--> opposite sides congruent (If the opposite sides are congruent it's a parallelogram). 2. Parallelogram--> consecutive angles are supplementary (If consecutive angles are supplementary, then it's a parallelogram). 3. Parallelogram--> opposite angles congruent (If the opposite angles are congruent the it's a parallelogram). 4. Parallelogram--> diagonals bisect each other (If the diagonals bisect each other then it's a parallelogram). These theorems can help you find the lengths of sides and diagonals as well as the measure of the angles. They can also help with proving if certain quadrilaterals are parallelograms by flipping these theorems around. (EX: Opposite sides congruent-->Parallelogram)
Lesson 4: Time for some shape knowledge! I'm sure you've heard of a rectangle, square, and rhombus before right? But do you really know what they are? Well, they're known as special parallelograms. This lesson will go over the properties and conditions of these special parallelograms. First, a rectangle is a quadrilateral with four right angles, a rhombus is a quadrilateral that has four congruent sides, and a square is both! Now, lets move forward! We will only be saying rectangle and rhombus but everything from the two shapes will apply to the square as well because of the it being both. Some more things to help distinguish the two is that for a rectangle the diagonals are congruent and for the rhombus, its diagonals are perpendicular and each one bisects a pair of opposite angles. As for the conditions, they are used to help prove a parallelogram to be a rectangle or rhombus
Theorem | Shape
-----------------------------------------------------------------------------------------------
1. One angle is a right angle. | Rectangle
2. Diagonals are congruent | Rectangle
3. One pair of consecutive sides are congruent | Rhombus
4. Diagonals are perpendicular | Rhombus
5. One diagonal bisects a pair of opposite angles. | Rhombus
Lesson 5: There's two other important shapes, trapezoid and kite, that we need to know and will be covering in this lesson. First, the trapezoid. A quadrilateral with a pair of parallel sides is a trapezoid and isosceles trapezoids are almost like isosceles triangles, where the legs are congruent, bases are congruent, and diagonals are congruent. On problems, the image or information(if provided) will most likely show or ask for the mid-segment of the trapezoid. To find the length mid-segment use this formula --> Length= 1/2(b1 + b2). You can also use this to find one of the base if the length is given but not one of the bases. Just substitute the numbers to where they belong in the formula and solve. Now onto the kite. A kite is a quadrilateral with exactly two pairs of congruent consecutive sides.
Lesson 7:
Lesson 8:
Lesson 9:
Lesson 2 and 3: No parallelograms aren't parallel gram crackers. Let's get a basic understand of what a parallelogram is and what will make something a parallelogram. There are four simple theorems. 1. Parallelogram--> opposite sides congruent (If the opposite sides are congruent it's a parallelogram). 2. Parallelogram--> consecutive angles are supplementary (If consecutive angles are supplementary, then it's a parallelogram). 3. Parallelogram--> opposite angles congruent (If the opposite angles are congruent the it's a parallelogram). 4. Parallelogram--> diagonals bisect each other (If the diagonals bisect each other then it's a parallelogram). These theorems can help you find the lengths of sides and diagonals as well as the measure of the angles. They can also help with proving if certain quadrilaterals are parallelograms by flipping these theorems around. (EX: Opposite sides congruent-->Parallelogram)
Lesson 4: Time for some shape knowledge! I'm sure you've heard of a rectangle, square, and rhombus before right? But do you really know what they are? Well, they're known as special parallelograms. This lesson will go over the properties and conditions of these special parallelograms. First, a rectangle is a quadrilateral with four right angles, a rhombus is a quadrilateral that has four congruent sides, and a square is both! Now, lets move forward! We will only be saying rectangle and rhombus but everything from the two shapes will apply to the square as well because of the it being both. Some more things to help distinguish the two is that for a rectangle the diagonals are congruent and for the rhombus, its diagonals are perpendicular and each one bisects a pair of opposite angles. As for the conditions, they are used to help prove a parallelogram to be a rectangle or rhombus
Theorem | Shape
-----------------------------------------------------------------------------------------------
1. One angle is a right angle. | Rectangle
2. Diagonals are congruent | Rectangle
3. One pair of consecutive sides are congruent | Rhombus
4. Diagonals are perpendicular | Rhombus
5. One diagonal bisects a pair of opposite angles. | Rhombus
Lesson 5: There's two other important shapes, trapezoid and kite, that we need to know and will be covering in this lesson. First, the trapezoid. A quadrilateral with a pair of parallel sides is a trapezoid and isosceles trapezoids are almost like isosceles triangles, where the legs are congruent, bases are congruent, and diagonals are congruent. On problems, the image or information(if provided) will most likely show or ask for the mid-segment of the trapezoid. To find the length mid-segment use this formula --> Length= 1/2(b1 + b2). You can also use this to find one of the base if the length is given but not one of the bases. Just substitute the numbers to where they belong in the formula and solve. Now onto the kite. A kite is a quadrilateral with exactly two pairs of congruent consecutive sides.
Lesson 7:
Lesson 8:
Lesson 9: