http://www.ck12.org Chapter 7. Similarity
- What is the scale factor of 4 ABCto 4 XY Z? Write the similarity statement.
- 4 ABC∼4MNP. The perimeter of 4 ABCis 150,AB=32 andMN=48. Find the perimeter of 4 MNP.
Answers:
- All the corresponding angles are congruent because the shapes are rectangles.
Let’s see if the sides are proportional. 128 =^23 and^1824 =^34.^236 =^34 , so the sides arenotin the same proportion, and the
rectangles arenotsimilar.
- All the sides are in the same ratio. Pick the two largest (or smallest) sides to find the ratio.
15
20
=
3
4
For the similarity statement, line up the proportional sides.AB→XY,BC→X Z,AC→Y Z,so 4 ABC∼4Y X Z.
- From the similarity statement,ABandMNare corresponding sides. The scale factor is^3248 =^23 or^32. 4 ABCis the
smaller triangle, so the perimeter of 4 MNPis^32 ( 150 ) =225.
Explore More
Determine if the following statements are true or false.
- All equilateral triangles are similar.
- All isosceles triangles are similar.
- All rectangles are similar.
- All rhombuses are similar.
- All squares are similar.
- All congruent polygons are similar.
- All similar polygons are congruent.
- All regular pentagons are similar.
- 4 BIG∼4HAT. List the congruent angles and proportions for the sides.
- IfBI=9 andHA=15, find the scale factor.
- IfBG=21, findHT.
- IfAT=45, findIG.
- Find the perimeter of 4 BIGand 4 HAT. What is the ratio of the perimeters?