Geometry

Similar Triangles

This assignment was to ratio the sides of the larger triangle to the smaller one to find the missing side. I divided one side of the larger triangle by the corresponding side of the smaller triangle. After the ratio has been created, I cross multiplied to end up with a inequality. I isolated and solved for the variable, and came up with the answer of 96 inches for side Ho.

I learned that this process is also used to find out if 2 triangles are similar to each other. If all 3 sides of both triangles have the same ratio, then they are similar to each other by the side-side-side(SSS) theorem. But, if the smaller triangle's sides are multiplied by the ratio, then you will end up with the larger triangle. The only way to correctly do this assignment is to match the sides of the triangle with the other.

In this assignment, I used proportions to find the length of the missing side. One side of the larger corresponds with another side of the smaller triangle. Once you set up the ratios, you cross multiply to end up with an inequality. After isolating the variable, your answer is the length of the once unknown side of the triangle.

Finding The Missing Side Using Angles

To find the missing sides of a triangle, I used a clinometer to measure the height of an object. I used trigonometry to find the lengths of side XY, XG, and XZ. I was only provided the values of 1 leg, and 2 angles of the triangle. I also had to use sine, cosine, tangent to find the missing sides by using the angles provided.

I made a story about a boy named Billy that got his drone stuck in a faraway tree, and my job was to find the hypotenuse of the right triangle. I included the angle of elevation and the length of 2 legs of the triangle. Based off of the values given, I had to use the tangent of trigonometry. I wanted to make a simple story along with a simple drawing so that I didn't spend much time focusing on the drawing, and instead worked on the math of it.

Birth Order vs. Personality Survey

I decided to research the correlation between birth order and personality so I created this survey. This is how my theories were set up:

Oldest - Convincing & Daring

Middle Child - Pleasantly Calm & Accommodating of Others

Youngest - Highly Sociable & Lively

Only Child - Analytical & Private

Two-Way Frequency Table Project

Using the data that I collected from the previous survey, I created four frequency tables. The first results table has the raw data from the survey while the remaining ones have percentages in decimal form. The percentages changed based off if it was by row, column, or overall total.

In the end, only one of my four theories matched up with what the data said. That was the only child and their personality of being analytical and private.

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