Scale Factors
This number tells you how much to multiply each dimension when creating a scaled copy of a figure.
What is a scale factor?
Under a dilation, angle measures have this relationship to the original angle measures.
What is they stay the same (are preserved/congruent)?
This similarity theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
What is AA (Angle-Angle) similarity?
In the proportion
a/b=c/d
the terms b and d are called this.
What are denominators?
These three types of transformations preserve both size and shape, making figures congruent.
What are rigid motions (translation, rotation, reflection)?
If triangle ABC has sides 6, 8, 10 and triangle DEF has sides 3, 4, 5, this is the scale factor from ABC to DEF.
What is 0.5 or 1/2?
When a line passes through the center of dilation, this happens to that line.
What is it remains unchanged (maps to itself)?
Triangle ABC has angles 30°, 60°, and 90°. For triangle DEF to be similar to triangle ABC, it must have these three angle measures.
What is 30°, 60°, and 90°?
If
x/6=8/12
, then x equals this value.
What is 4?
To prove two figures are similar, you must show there exists a sequence of these types of transformations.
What are rigid motions and dilations?
A rectangle with dimensions 4 by 6 is dilated by a scale factor of 2.5. These are the new dimensions.
What is 10 by 15?
When a line does NOT pass through the center of dilation, the image line has this relationship to the original line.
What is parallel?
In similar triangles, this is the relationship between corresponding angles and corresponding sides.
What is corresponding angles are congruent and corresponding sides are proportional?
In triangle ABC with line DE parallel to BC, if AD = 5, DB = 10, and AE = 3, then EC equals this.
A figure is translated 3 units right, then dilated by a scale factor of 0.5. The final image has this relationship to the original.
What is similar but not congruent?
Two similar pentagons have corresponding sides in the ratio 3:7. If the smaller pentagon has a perimeter of 45, this is the perimeter of the larger pentagon.
What is 105?
Under a dilation with scale factor 3, a circle with radius 4 will have this new radius.
What is 12?
Triangle RST has sides 9, 12, and 15. Triangle UVW has sides 6, 8, and 10. These triangles have this relationship.
What is they are similar (with scale factor 2/3)?
Two similar rectangles have areas in the ratio 4:9. The ratio of their corresponding side lengths is this.
What is 2:3?
Triangle ABC is reflected over the y-axis, then rotated 90° clockwise, then dilated by a scale factor of 2. The number of transformations that preserve congruence is this.
What is 2 (reflection and rotation are rigid motions)?
If a dilation with scale factor k takes point (4, -2) to point (10, -5), this is the value of k.
What is 5/2 or 2.5?
If point P is the center of dilation with scale factor k, and point A maps to point A', then these three points have this special relationship.
What is they are collinear (P, A, and A' lie on the same line)?
If triangles ABC and DEF are similar with ∠A ≅ ∠D and ∠B ≅ ∠E, and AB = 8, BC = 12, DE = 6, then EF has this length.
What is 9?
If triangles PQR and STU are similar with a scale factor of 3/4, and the perimeter of triangle PQR is 36, then the perimeter of triangle STU is this.
What is 27?
Figure A undergoes only rigid motions to become Figure B, then Figure B undergoes a dilation to become Figure C. The relationship between Figures A and C is this.
What is they are similar (but A and B are congruent)?