## SOL Objective(s):

**7.6 The student will determine whether plane figures – quadrilaterals and triangles – are similar and write proportions to express the**

relationships between corresponding sides of similar figures.

relationships between corresponding sides of similar figures.

## Note:

This objective deals with the basics of identifying corresponding attributes of similar figures. This skill is used to solve problems with proportional reasoning. Additional information and application of this skill will be found under Computation and Estimation, then Solving Problems with Proportional Reasoning, and then Problems with Similar Figures.

## Khan Phrases:Similar Triangles 1
Similar Triangles 2 Solving Similar Triangles 1 Solving Similar Triangles 2 Solving problems with similar and congruent triangles |

## The Basics and Background Information:

- Two polygons are similar if corresponding (matching) angles are congruent and the lengths of corresponding sides are proportional.
- Congruent polygons have the same size and shape.
- Congruent polygons are similar polygons for which the ratio of the corresponding sides is 1:1.
- Similarity statements can be used to determine corresponding parts of similar figures such as:

∠ A corresponds to ∠ D

AB corresponds to DE

- The traditional notation for marking congruent angles is to use a curve on each angle. Denote which angles are congruent with the same number of curved

- Congruent sides are denoted with the same number of hatch marks on each congruent side. For example, a side on a polygon with 2 hatch marks is congruent to the side with 2 hatch marks on a congruent polygon.

## Essential Knowledge and Skills:

- Identify corresponding sides and corresponding and congruent angles of similar figures using the traditional notation of curved lines for the angles.
- Write proportions to express the relationships between the lengths of corresponding sides of similar figures.
- Determine if quadrilaterals or triangles are similar by examining congruence of corresponding angles and proportionality of corresponding sides.
- Given two similar figures, write similarity statements using symbols such as Δ ABC ~ Δ DEF , ∠ A corresponds to ∠ D, and AB corresponds to DE .

## Vocabulary and Things to know:similar
corresponding congruent how angles are marked to indicate different measurements how sides or segments are marked to indicate different measurements the difference between congruent and similar |
## Be Able to:identify and label line segments and angles
use traditional mathematical symbols to indicate angles and line segments identify corresponding sides (no matter how the figures are oriented) |

The video above from Khan Academy reviews important key vocabulary with regard to similar shapes, and correstponding sides and angles. It is important, before using any proportion to know which sides are corresponding.

The way in which the proportion is solved is different than what was shown in class, so if there are any questions, feel free to ask questions OR use the proportion and solve the proportion in a way you understand, maybe such as cross multiply and divide or think of equivalent fractions, if the numbers lend themselves to mental math.

Proportions with similar figures youtube presentation above shows the basic thinking, but not the proper way of showing your thinking in an algebraic equation. Great for a short video on the basic thinking.

The youtube video above shares basic understanding as well as essential vocabulary that pertains to similar shapes.

Just another example from a different source.