# G.7 - Similarity

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

### 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

2016 VDOE Curriculum Framework - G.7 Understanding

·  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

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

·  G.73  Use direct proofs to prove triangles similar.

·  G.71  Prove two triangles similar given relationships among angles and sides of triangles expressed numerically or algebraically.

·  G.72  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: Aug 23, 2018