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.7 The student, given information in the form of a figure or statement, will prove two triangles are similar.
Bloom's Level: Evaluate
- 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
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
- 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-Side-Side (SSS); and
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).
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