## Triangles (Similarity and Congruence)

#### Aligned To Common Core Standard:

**Trigonometry** - HSG-SRT.C.6

What is the Difference between Similarity and Congruence of Triangles?
In mathematics, shapes, angles, and proportions help in explaining the difference between similarity and congruence.
Congruent figures coincide with each other and show the same measurements when superimposed. Two congruent shapes have the same size and shape but their orientation can differ.
Similarity means to resemble closely with each other but not being identical. Similar objects can be the same in shape but their sizes are different.
**CONGRUENT TRIANGLES** - Congruent triangles are identical in both shapes and sizes. The angles and sides of one triangle will be identical to the corresponding angles and sides of another triangle. That means that if one triangle is superimposed on another triangle, they perfectly coincide with each other.
**PROPERTIES OF CONGRUENT TRIANGLES** - SSS Congruency: SSS stands for 'side, side, side'. Two triangles are congruent when all three sides of one triangle are equal to the corresponding three sides of another triangle
SAS Congruency: SAS stands for 'side, angle, side'. Two triangles are Sadie to be congruent if two sides and the included angle of one triangle coincide with the corresponding two sides and included angle.
ASA Congruency:ASA stands for 'angle, side, angle'. Two triangles are said to be congruent if two angles and any one side of one triangle coincide with corresponding two sides and any one angle of another triangle.
**SIMILAR TRIANGLES** - Two triangles are similar if all their angles are equal and the corresponding sides share the same ratio. There are three ways to prove the similarity of triangles: AA, SAS, SSS
**PROPERTIES OF SIMILAR TRIANGLES** - AA Similarity: AA stands for 'angle, angle'. It means that if two triangles are said to be similar to two angles of one triangle are equal to the two angles of another triangle.
SAS Similarity: SAS stands for 'side, angle, side'. It means that two triangles are said to be similar when:
- the ratio between sides is equal to the ratio between another two sides, i.e., two pairs of sides are in equal ratio.
- Included angles are equal.
SSS Similarity: SSS stands for 'side, side, side'. Two triangles are similar if they have all three pairs of sides in the same ratio. This selection of worksheets and lessons shows students how identify and use triangles that are similar and/or congruent.

### Printable Worksheets And Lessons

- Using Similarity
Step-by-step Lesson - This begins to show you the possibilities
of using similarity.

- Guided Lesson
- These work together well. You should have a solid understanding
of the concepts after you complete this one.

- Guided Lesson Explanation
- The triangle theorems pop back into play with these.

- Practice Worksheet
- I felt that I had to spread the problems out greatly to make sure
that they were clear to read.

- Matching Worksheet
- Match the parts together to make it work best.

- Identify Similar Triangles
with Proofs 5 Pack - Triangle proofs that all students dream
about at night. Sometimes they are nightmares.

- Similarity Worksheet Five Pack
- I really like the potpourri of problems that I present to you
here.

- Similarity of Triangles In Numeric
Problems Worksheet Five Pack - We mostly focus on finding the
sides of triangles, but we throw some real world problems in there.

#### Homework Sheets

Using similarity, you are asked to find missing sides and angles.

- Homework 1 - If the angles fit they are congruent, if they don't they aren't.
- Homework 2 - These triangles are similar and the similarity statement is true.
- Homework 3 - ΔDEF ~ ΔABC means that ΔDEF is similar to ΔABC. And the sides of similar triangles are proportional.

#### Practice Worksheets

The skill covered completely over the course of these worksheets.

- Practice 1 - Locate the matching sides and go from there.
- Practice 2 - The AA similarity theorem states that two triangles are similar if and only if two angles of one triangle are congruent to two angles of the other triangles.
- Practice 3 - In the given triangles below, ΔABC ~ ΔDEF. Find the missing length.

#### Math Skill Quizzes

You should try to always verify your answer when doing these types of problems by using two different methods.