Proportions & Algebra
Solve:
12/x = 30
x= 5 2 or 0.4
A dilation image can be smaller than the original.
True - Magnitude or (scale factor) can be less than 1.
If two angles of one triangle equal two angles of another, what theorem applies?
AA Similarity
In similar triangles, what is the relationship between corresponding altitudes?
They have the same ratio as corresponding sides.
Two triangles are similar and the scale factor from the small triangle to the large triangle is 5/3. If the perimeter of the small triangle is 45, what is the perimeter of the large triangle?
75
5x=3(x+6)
x=9
Corresponding altitudes of similar triangles are equal.
False (they are proportional)
If two sides including an angle are proportional and the angle is equal, what theorem applies?
SAS Similarity
Two similar triangles have side ratio 3:5. What is the ratio of their perimeters and altitudes?
3:5
Two similar figures have an area ratio of 9:25. If the smaller figure has area 36, what is the area of the larger figure?
100
A building must satisfy
h/w = 3/2
If the street is 60 ft wide, how tall may it be?
90 ft
If two right triangles share one equal acute angle, they are similar.
True (AA)
If all three sides are proportional, what theorem applies?
SSS Similarity
Two similar triangles have side ratio 2:3. What is the ratio of their areas?
4:9
A line parallel to one side of a triangle divides one side into segments 6 and 9. The whole side is 15. What is the ratio of the matching segments on the other side of the triangle?
2:3
(x-4)/(x+2) = 3/5
x=13
Equal corresponding angles guarantee two quadrilaterals are similar.
False (side ratios must also match)
Why does AA automatically give proportional sides?
Because the triangles are similar by definition
The altitude of a small triangle is 4 and the scale factor is 2. Find the altitude of the larger triangle and the ratio of their areas.
Altitude = 8, area ratio = 1:4
A right triangle contains a square touching all three sides, creating several smaller triangles inside the figure. What theorem explains why all of those triangles are similar?
AA Similarity (Daily Double if you can explain why)
18/x=x/2
x = +-6
If a line parallel to one side of a triangle cuts the other two sides, it divides them proportionally.
True (Side-Splitter Theorem)
Two triangles are similar to the same triangle. What must be true about them?
They are similar to each other (Corollary to AA)
Two similar triangles have area ratio 16:25. Find the ratio of their sides, altitudes, and perimeters.
4:5
Explain how perimeter and area scale.
Perimeter scales linearly, lengths changes by scale of r; area scales quadratically by two dimensions, so it scales by r2. (Daily Double - what does r represent)