Geometry All Around Us
By: Dylan Conley
Period 1 Geometry
The theme is football stadiums!!!
1. SSS. Side Side Side is the answer because if DA and BC are congruent that is one side. If DC and BA are congruent then that is another side. Then you would use the side they share, AC, to be the last side. That is why the answer is SSS.
2. Parallel. The answer is parallel because the lines will never intersect. Also because they will always be the same distance apart. That is why the answer is parallel .
3. Isosceles, Acute. The answer is acute because the angles are acute. It is isosceles because two of the sides are congruent. That is why it is acute, isosceles.
4. (3,5.5). The answer is (3,5.5) because you would use the midpoint formula to plug in the two points. First you would do 4+2 divided by 2 to find your x value. Then you would do 8+3 divided by 2 to find the y value. Then you use the values you found to put together an ordered pair. That is why the answer is (3,5.5).
5. Supplementary. The answer is supplementary because supplementary is when two angles add up to 180 degrees. The reason why these angles are supplementary is because a straight line is 180 degrees. These two angles added together create a straight line. Therefore, these two angles equal 180 degrees and are supplementary.
6. Yes, alternate interior angles are congruent. You can prove these lines parallel because of alternate interior angles. The reason is because when proving line parallel you could know by having alternate interior angles being congruent. In this image they are congruent. Therefore, you know the lines are parallel by having alternate interior angles congruent.
7. x=21. The problem was AB equals 3x and BC equals x and AC equals 84. What would x be equal to? You would start by adding up AB and BC because those two added together create AC. So, you would know that those two added together equal 84. You would set up the problem like this... 3x + x= 84. You would simplify it by adding x to 3x. Then you get this... 4x = 84. Then you would divide by 4 on each side to get 21.
8. x=20. x equals 20 because you know that the sum of the two angles are a right triangle as shown by the green box. Therefore, you would add the two angles together and set them equal to 90 because that is what a right angle equals. Then you would solve it algebraically to get 20.
9. The measure of AC= 13. For this problem you would use the Pythagorean theorem. The formula is a squared + b squared = c squared. 12 would be A, 5 would be B and AC would be C. You would square 12 and 5 and add them together. You would get 169. Then you would know c squared = 169. However, you are not done yet. You would need to take the square root of 169 to get the final answer because it is being squared. You need to take the reverse (square root) to find the real answer. So, you would get AC = 13.
10. SAS. It is Side Angle Side because your first side in EC being congruent to AC. The angle is the vertical angles of angle EDC and angle ABC. The last side in DC being congruent to BC. That is why the answer is SAS.