Dilation
What is the term for a transformation that changes the size of a figure?
What is dilation?
What does AA stand for in the AA Similarity Theorem?
What is Angle-Angle?
What is the relationship between corresponding sides of similar triangles?
What is they are proportional?
When using similar triangles, what do we call the sides that correspond to each other?
What are corresponding sides?
What does it mean to partition a segment?
What is to divide a segment into parts?
A triangle is dilated with a scale factor of 2. If a side of the original triangle is 5 cm, what is the length of the corresponding side in the dilated triangle?
What is 10 cm?
If two triangles have two pairs of congruent angles, are they similar?
What is yes?
If two triangles are similar, how are their corresponding angles related?
What is they are congruent?
If two triangles are similar and the ratio of their corresponding sides is 3:1, and a side in the larger triangle is 12 cm, what is the corresponding side in the smaller triangle?
What is 4 cm?
What is a ratio?
What is a comparison of two quantities?
Describe the effect of a scale factor of 1/3 on a figure
What is a reduction to 1/3 of the original size?
State the SSS Similarity Theorem.
What is if the corresponding sides of two triangles are proportional, then the triangles are similar?
A line parallel to one side of a triangle divides the other two sides how?
What is proportionally?
A 6-foot tall person casts a 4-foot shadow. If a nearby tree casts a 20-foot shadow, how tall is the tree?
What is 30 feet?
Point P partitions segment AB in the ratio 1:2. If AB = 9 cm, what is the length of AP?
What is 3 cm?
Triangle ABC is dilated with a center at the origin and a scale factor of 3. If A(1, 2), what are the coordinates of A'?
What is (3, 6)?
In triangles ABC and XYZ, angle A = angle X, AB/XY = AC/XZ. Are the triangles similar? If so, by what theorem?
What is yes, by SAS Similarity Theorem?
Explain how similar triangles are used to prove theorems about proportional segments.
What is by setting up ratios of corresponding sides?
Explain how similar triangles can be used to find the height of a building indirectly.
What is by measuring shadows and using proportions?
Point P partitions segment AB in the ratio 2:3. If A(1, 4) and B(6, 9), find the coordinates of P.
What is (3, 6)?
Describe a sequence of transformations to map a figure to its dilated image that has also been reflected.
What is a dilation followed by a reflection?
Given a diagram of overlapping triangles, prove they are similar using one of the similarity theorems.
(This will require a diagram, and the answer will depend on the provided diagram. The answer should include the theorem used and the steps of the proof.)
Provide a brief proof that a line parallel to one side of a triangle divides the other two sides proportionally.
(This will require a diagram and a written proof.)
Describe a real world situation where calculating corresponding parts of similar triangles is useful.
(Answers can vary: examples include map scaling, architectural design, photography, etc.)
Explain how to find the coordinates of a point that partitions a segment in a given ratio.
What is using the section formula or proportional reasoning with the coordinates?