Geo Semester Review
Table of Contents
- Area of Triangles, Rectangles and Parallelograms.
- Area
- Lines and Transversals
- Lines and transversals
- Distance formula and the coordinate plane
- Distance Formula and the Coordinate Plane
- Basic Angle Relationships
- Liner angles
- Supplementary
- Complementary Angles
- Vertical Angles
- Congruent
- Corresponding Sides
- Corresponding sides
Area
Introduction
In this section, we will learn how to find the area of triangles, trapezoids and other parallelograms. We will also learn how to find the height of these shapes. The basic equation for area is a = bh ("b" being base and "h" being height) all equations to follow are essentially based off this.
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Finding the height of a triangle + Trapezoid
To find the height of a triangle, generally, it will be labelled with "h" going from the base to the top vertex. When not available, you can use a couple different equations. Pythagorean theorem, in my opinion, is the best equation to use but you do need two side lengths and a right angle
Area of triangles
To find the area of a triangle you have to do the equation 1/2 bh. This equation is one-half the base multiplied by the height. We know this because a triangle is 1/2 of a square/rectangle.
Finding the area of a trapezoid
To find the area of a trapezoid, one must do the equation A= the sum of base 1 and base 2 divided by two. Multiplied by the height. Base 1 is the bottom base and base 2 is the top base.
Finding the Area of a Parallelogream
When finding the area of a parallelogram, you use the equation A=bh since it is essentially a square/rectangle, just transformed. The height of the parallelogram runs from the bottom base to the top base and you just use the base measurement. Ex. Base = 2 height = 5...... A = bh, = 2 x 5. A= 10
All shapes are made up of triangles
All shapes are made up of triangles. For example, an equilateral square is made up of two right triangles. It's why in the equation to find the area of a triangle, it uses 1/2 the bh. If one just calculated the area of a square it would be (b)(h) but since a square is made up of two right triangles, it's 1/2
Lines and transversals
Introduction
Lines are straight lines that may go for a specific length or infinite. Transversals are the lines which intercept two parallel lines.
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Parallel Lines + Transversal
This example shows two parallel lines then one transversal. This demo shows vertical angles, supplementary angles, and alternate interior angles. Vertical angles are the angle on the opposite side of the vertices. Supplementary angles are two angles which add up to 180 degrees. alternate interior angles are angles on alternate sides, on the interior of the parallel lines. A transversal is a line which goes through two (or more) parallel lines. There can also be multiple transversals
Angle Relationships
[br]Vertical Angles :[br]Vertical Angles are a pair of non-adjacent angles made by a transversal and vertices. [br][br]Corresponding Angles : [br]Corresponding Angles are angles at the same location on the line but in a different section.[br][br]Alternate Exterior Angles:[br]Alternate Exterior Angles are angles on the outside of the transversal on opposite sides[br][br]Alternate Interior Angles :[br]Angles in the interior of the two parallel lines on opposite sides of the transversal.[br][br]
Parallel Lines and Angles
We know that a pair of parallel lines and a transversal create the same angles on both lines where the transversal intersects with the parallel lines.
Distance Formula and the Coordinate Plane
Distance Formula
Distance Formula Explanation
The distance formula is used to determine the distance, f, between two points. ... The distance formula is derived by creating a triangle and using the Pythagorean theorem to find the length of the hypotenuse. But in this explanation, you use the two points that you were given and make the two sides of the right triangle then rooting the two sides to lead into the Pythagorean Theorem.[br](ex.)- Timmy saw a bird fly to the top of the tree (8,6) from where he was standing (1,2). How far did the bird fly?
Distance Formula (Pythagorean Theorem)
Distance Formula (Pythagorean Theorem) Explanation
For this explanation, we use the Pythagorean Theorem. This formula is.[math]A^2+B^2=C^2[/math] This formula can only be used on right triangles. The formula correlates A, B, and C to different sides on the triangle. C being the hypotenuse. With this formula, you plug in the two sides that you have and you can then square them, add them together and the root them back to get the answer.[br](ex.)Timmy saw a bird fly to the top of the tree from where he was standing. He knew that the tree was 4 units high and was 7 units away from him. How far did the bird fly?
Liner angles
Corresponding sides
Corresponding sides
In triangles that are corresponding, they are exactly the same in every way except location, while triangles that are similar are proportional, and can be of different size and orientation. The triangles are similar and congruent because of SSS.