Ch. 8 Always, Sometimes, Never
Two right triangles are similar.
- sometimes
What two things do similar polygons have?
- Corr. angles must be congruent. - The ratios of the core. sides must be congruent.
Reduction
- From big to small
Dilation
- From small to big *Enlargement
Two equilateral polygons are similar.
- Sometimes
Two rectangles are similar if neither is a square.
- Sometimes
Means-Extremes Products Theorem
a:b=c:d In a proportion, the product of the means is equal to the product of the extremes
Two equilateral triangles are similar.
- always
Two issues. triangles are similar if their vertex angles are congruent.
- always
Two issues. triangles are similar if they have a pair of base angles.
- always
Two right triangles are similar if the legs of one are proportional to the legs of another.
- always
An equilateral triangle is similar to a scalene triangle.
- never
An obtuse triangle is similar to an acute triangle.
- never
The geometric mean of two whole numbers is 0.
- never
If the ratio of the measures of a pair of corn. angles of two polygons is 3:4, then the ratio of the polygons' perimeter is 5:6.
- sometimes
Two equiangular polygons are similar.
- sometimes
Means-Extremes Ratio Theorem
If the product of a pair of nonzero number's is equal to the product of another pair of nonzero numbers, then either pair of numbers may be made the extremes, and the other pair the means, of a proportion.
If the ratio of the perimeter of two triangles is 1:2, then the triangles are similar.
- sometimes
If two triangles are similar, then they are congruent.
- sometimes
If two regular polygons have the same number diagonals, then they are similar.
- always
If two triangles are congruent, then they are similar.
- always
If two sides of a triangle are proportional to two sides of another triangle, then these two triangles are similar.
- sometimes
Two isos. triangles with congruent bases are similar.
- sometimes
Two issues. triangles are similar if they have a pair of congruent angles.
- sometimes
