Math - 2018-19
G.7 - Similarity
G.7 The student, given information in the form of a figure or statement, will prove two triangles are similar.
- 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
· 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
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
· G.73 Use direct proofs to prove triangles similar.
two triangles similar given relationships among angles and sides of triangles
expressed numerically or algebraically.
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