How do I use proportionalrity theroms to solve geometric problems?

Proportionalrity means when two variables whose ratio is constant or forming a relationship with other parts or quantities; being in proportion.Properly related in size, degree, or other measurable characteristics, which can also be known as corresponding. When there are little triangles on a horizontal line, then that means the lines are parallel to eachother. There are three types of theroms you could use. The Triangle proportions ality therom, triangle proportional ality therom converse, and the theroms of proportionality.
A proportion is a name we give to a statement that two ratios are equal. It can be written in two ways:

• two equal fractions,

  or,

• using a colon,    a:b = c:d

When using porprotions, you can use them to test weather the ratios are equal to eachother. You can also use porprotions when looking for a missing term in a proportion. First, write the proportion, using a letter to stand for the missing term. Some examples would be:

• If an object travels at a constant speed then the distance traveled is proportional to the time spent traveling, with the speed being the constant of proportionality.

How do I use the pythagream therom to solve geometric problems?

Something that can help you when using the pythagream therom can be by using each step. Step one would be number the triangles from smallest to largest, with roman numerals, and then you well need to redraw each of the triangles seprately. Step two redraw the triangles and make you sure the right angle is on the right side and then name each triangle with the roman numeral. Step three is labeling the vertices. Step four is making sure you have a similarity statement. And last but not least you will need to set up the proportions using corresponding sides. This theorem is useful to determine one of the three sides of a right triangle if you know the other two.
In every congruent triangle: there are three sets of congruent sides and there are three sets of congruent angles. Squares on the legs of a right triangle add up to the square on the hypotenuse.

How do I use properties of similar triangles to solve geometric problems?

The Pythagrean therom includes, C= hypotenuse which is also known as the longest side and is always on the opposite side of the right angle. There are many types of theroms such as of course the pythagrean therom, phythagrean therom converse, acute triangle therom, and the obtuse triangle theorm. An example of an acute triangle would be if C squared is less than A squared plus B squared. And and example of the obtuse triangle therom wuld be if C squared is greater than A squared plus B squared. In any right triangle, the area of the hypotenuse is equal to the sum of the squares whose sides are the two legs. The equation is c2 (squared)= a2 (squared)+ b2 (squared). A and B should be the shortest sides and C should be the longest.  

How do i set up ratios and properties to solve the geometric problems?

 A ratio can be width over length. The width is the shortest side and the length can be known as the longest side. Another way a ratio can be presented is ratio=ratio which is using corresponding parts.Ratios are indicated also by writing the two values with a colon between them. For example 3 to 9 can also be expressed as 3:9. A ratio is also a number relating two numbers or two quantities of the same kind. When one ratio is set equal to another ratio, it is said that they are proportional. You can also try setting up porprotions while using word problems when you might be using two comparisions
Porportions are two ratios that equal eachother. When using or setting up proportions you may have similiar triangles and sometimes one of the parts of the proportion is missing.  Similiar means same shape, but different sizes.

How do I use properties of congruence to find unknown values?

Always list the corresponding vertices in the same order. You might want to know if the angles are congruent or not for one to be able to solve your problem. Also all the angles MUSt equal to 180 degrees. When you are working with isosceles trianlges, you will always have a vertex angle, one leg on each side of a triangle, a base angle and a base. The Base angle Therom means if all the sides are congruent then the angles will be congruent. Base Angle Converse means if the bass is congruent, then the legs are congruent.Base Angle therom-Corollary, if a triangle is equilateral, then it is equilangular and The Base angle converse-Corollary, if a triangle is equilanglar, then it is equilaterial. When you are looking for properties of congruence, you will be looking for a congruent statement, corresponding angle and corresponding sides.

How do I use triangle sum properties to find unknown values?

One way to be able to use the triangle some properties to find unknown values can be by being able to classify a triangle either by its sides or angles. For example some of these trianlges that are classified by its sides are scalene which have no congruent sides, isosceles, at least two congruent sides and the equilateral triangle which all three sides are congruent and some of the triangles that are classified by angles are the acute, obtuse,equiangular and right triangles. They all share a vertex. Such angles are equal in measure and can be described as congruent. Also something important you should remember is that the sum of the three angles in a triangle is always 180 degrees, A+B+C=180. Exterior angles of triangles- Angles that form linear pairs with the interior angles. Some of the different terms when you are lokking for trinagle sum properties are Interior Angles Of triangles, Triangle Sum Therom, Corollary, and the Exterior Angles Therom.

How do I write linear equations passing through a given point?

A linear euation is an equation whose graph is a line.First while solving or trying to write linear equations, you MUST know your x and y intercept. The x value is always undefined and is the vertical line and the y value is ZERO and is the horzontial line on a graph. You also have to remember the x is the indepenedent variable and the y is the depenedent. The x intercept is a point on a line that touches the x-axis (always at the coordinate point) (X,0). The y intercept is a point where a line touches the y-axis (Y,0).
While solving a linear equation you may need to use slope intercept form which is y=mx+b or either standard form which is Ax+By=C but standard form may also be changed to slope intercept form. When you are graphing points that are perpendicular that pass through a line, you need to find the slope, make it into a fraction, change the reciprical and then change the sign.