http://www.ck12.org Chapter 7. Similarity
Vocabulary
Similar polygonsare two polygons with the same shape, but not necessarily the same size. The corresponding
angles of similar polygons arecongruent(exactly the same) and the corresponding sides areproportional(in the
same ratio). In similar polygons, the ratio of one side of a polygon to the corresponding side of the other is called
thescale factor.
Guided Practice
1.ABCDandUV W Xare below. Are these two rectangles similar?
- 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.
Practice
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?
Use the picture to the right to answer questions 14-18.
- Findm^6 Eandm^6 Q.
15.ABCDE∼QLMNP, find the scale factor.