#### Math - 2017-18

# G.7 and *G.7 - Similarity

**G.7** The student, given
information in the form of a figure or statement, will **prove **two triangles are
similar, using algebraic and coordinate methods as well as deductive proofs.

G.7The student, given information in the form of a figure or statement, willprovetwo triangles are similar.

**Bloom's Level: ** Evaluate

*Adopted: 2009*

### BIG IDEAS

- I can determine if a fence at the zoo is high enough to
contain a giraffe, if a river gorge is too wide to jump with my bike, if the
angle I hold my tennis racket will get the ball over the net, and if a camera
lens will zoom close enough to get a clear shot of Taylor Swift. I can find the height of a tree by measuring shadows.

- I will know
that congruence describes a special similarity relationship between objects and
is a form of equivalence, and will apply to new situations some techniques for
finding solutions.

### UNDERSTANDING THE STANDARD

- Similarity has real-world applications in a
variety of areas, including art, architecture, and the sciences.
- Similarity does not depend on the position of
the triangle.
- Congruent figures are also similar, but similar
figures are not necessarily congruent.

· Deductive or inductive reasoning is used in mathematical proofs. In this course, deductive reasoning and logic are used in direct proofs. Direct proofs are presented in different formats (typically two-column or paragraph) and employ definitions, postulates, theorems, and algebraic justifications including coordinate methods.

· Similarity has practical applications in a variety of areas, including art, architecture, and the sciences.

· Similarity does not depend on the position of the triangles.

· Similar triangles are created using dilations.

· Congruent figures are also similar, but similar figures are not necessarily congruent.

· Corresponding sides of similar triangles are proportional.

· Corresponding angles of similar triangles are congruent.

· The altitude in a right triangle creates three similar right triangles.

· Two triangles can be proven similar using the following criterion:

Side-Angle-Side (SAS);

Side-Side-Side (SSS); and

Angle-Angle (AA).

### ESSENTIALS

**Review
Solving for Variables within Proportions**

G.7_{1} **Use** definitions, postulates, and
theorems to **prove** triangles similar.

·
G.7_{3} **Use**
direct proofs to **prove** triangles
similar.

G.7_{2} **Use**
algebraic methods to **prove** that
triangles are similar.

·
G.7_{1} **Prove**
two triangles similar given relationships among angles and sides of triangles
expressed numerically or algebraically.

G.7_{3} **Use**
coordinate methods, such as distance formula, to **prove** 2 triangles are similar.

·
G.7_{2} **Prove**
two triangles similar given representations in the coordinate plane and using
coordinate methods (distance formula and slope formula).

### KEY VOCABULARY

prove,
triangle, similar, algebraic method, coordinate method, deductive proof,
postulate, theorem, Angle-Angle Similarity, Side-Side-Side Similarity,
Side-Angle-Side Similarity, distance formula, position, congruent

*Updated: Dec 14, 2017*