Ratio and Proportion

Let us learn about ratio and proportion,
Ratio is a concept that you have probably encountered in other math classes. It is a comparison of sizes.

Ratio :

The ratio of two numbers a and b is the fraction , usually expressed in reduced form. An alternative form involves a colon. The colon form is most frequently used when comparing three or more numbers to each other. See Table 1 .

TABLE 1 Ratio Formats Ratio Written Form 3 to 4 3/4 or 3 : 4 a to b, b ≠ 0 a/b or a : b 1 to 3 to 5 1 : 3 : 5

Example 1: A classroom has 25 boys and 15 girls. What is the ratio of boys to girls?




The ratio of boys to girls is 5 to 3, or 5/3, or 5 : 3.
Example 2: The ratio of two supplementary angles is 2 to 3. Find the measure of each angle.

• The angles have measures of 72° and 108°.
  
• 2 x to 3 x reduces to 2 to 3.
  
• 2 x + 3 x = 180° (The sum of supplementary angles is 180°.)
  
• 5 x = 180°
  
• x = 36°
  
• Then, 2 x = 2(36°) and 3 x = 3(36°).
  
• So, 2 x = 72° and 3 x = 108°

The angles have measures of 72° and 108°.

Hope the above explanation helped.

Perimeters and Areas of similar triangles

Let us learn about perimeters and areas of similar triangles,
When two triangles are similar, the reduced ratio of any two corresponding sides is called the scale factor of the similar triangles. In Figure 1 , Δ ABC∼ Δ DEF.

Figure 1 Similar triangles whose scale factor is 2 : 1.

The ratios of corresponding sides are 6/3, 8/4, 10/5. These all reduce to 2/1. It is then said that the scale factor of these two similar triangles is 2 : 1.
The perimeter of Δ ABC is 24 inches, and the perimeter of Δ DEF is 12 inches. When you compare the ratios of the perimeters of these similar triangles, you also get 2 : 1. This leads to the following theorem.
Theorem : If two similar triangles have a scale factor of a : b, then the ratio of their perimeters is a : b.
Hope the above explanation helped you.

Classifying Triangles by Sides or Angles

Let us study classifying triangles by sides or angles,
Triangles can be classified either according to their sides or according to their angles. All of each may be of different or the same sizes; any two sides or angles may be of the same size; there may be one distinctive angle.


The types of triangles classified by their sides are the following:



1. Equilateral triangle: A triangle with all three sides equal in measure. the slash marks indicate equal measure.

2. Isosceles triangle: A triangle in which at least two sides have equal measure

3. Scalene triangle: A triangle with all three sides of different measures


The types of triangles classified by their angles include the following:





1. Right triangle: A triangle that has a right angle in its interior

2. Obtuse triangle: A triangle having an obtuse angle (greater than 90° but less than 180°) in its interior.

3. Acute triangle: A triangle having all acute angles (less than 90°) in its interior

4. Equiangular triangle: A triangle having all angles of equal measure.

Hope the above explanation helped you, now let me explain polygons.