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

Bloom's Level:  Evaluate

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.71  Use definitions, postulates, and theorems to prove triangles similar.

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

G.72  Use algebraic methods to prove that triangles are similar.

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

G.73  Use coordinate methods, such as distance formula, to prove 2 triangles are similar.

·  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: Dec 14, 2017