Dilations
If a figure is dilated by a scale factor of 2, what happens to its side lengths?
They double.
What’s the scale factor from side length 5 to 15?
3
Two triangles have all corresponding sides equal. Are they congruent?
Yes.
What does it mean for two polygons to be similar?
Corresponding angles equal and corresponding sides proportional.
If two angles of one triangle equal two angles of another, are they similar?
Yes, by AA similarity.
A triangle is dilated by a factor of ½. One side is 10 cm. What is its image’s side length?
: 5 cm.
Map scale 1 in = 20 mi. If map measurement is 3 in, how many miles is that?
60 mi.
What must correspond between two shapes to conclude congruence?
All sides and all angles equal.
Are rectangles 4×6 and 6×9 similar? Why?
Yes; side ratios both 2:3.
Triangles with sides 3,4,5 and 6,8,10 — congruent, similar, or both?
Similar
The scale factor is 1.5. Original side = 8. What's new side length?
12 cm.
A rectangle has sides 4×6, a similar rectangle has sides 10×15. What’s the scale factor?
2.5.
Can two figures be congruent if only two pairs of sides are equal and one angle equal?
Not necessarily — depends if angle is included, etc.
Ratio of corresponding sides of two similar triangles is 5:3. If smaller triangle’s side = 9, what’s corresponding side in larger?
15.
Given two triangles, one has sides 7,24,25, other has 14,48,50. Are they similar?
Yes, by SSS (scale factor 2).
A dilation will always make the copy larger
False. A dilation can make it smaller or the same size
A triangle is enlarged by scale factor 1.2. Original perimeter 50. What’s new perimeter?
60.
Given triangle ABC is congruent to triangle DEF, write a congruence statement.
ABC ≅ DEF.
If scale factor is 4:1 from small to big, and small perimeter = 12, big perimeter = ?
48.
Triangle A angles: 40°, 80° x. Triangle B angles:80°, 60°, x. Are they similar?
Yes
Draw or describe the dilation of (0,0), (2,1) by factor 3 around origin.
(0,0), (6,3).
Downward line with a rise of 3 and a run of 1
How can you tell if 2 lines have the same slope?
They are parallel
If you don't have a grid to count, how can you tell if 2 lines are parallel and have the same slope?
Use a straight edge to compare
How do you use a right triangle to find the slope of the line?
Use the rise and the run to count. Make a fraction of the y number over the x number and simplify