What if you were comparing a baseball diamond and a softball diamond? A baseball diamond is a square with 90 foot sides. A softball diamond is a square with 60 foot sides. Are the two diamonds similar? If so, what is the scale factor?
Similar Polygons and Scale Factors
These polygons are not similar:
Understanding a Similarty Statement
Solving for Unknown Vlaues
Solving for the Scale Factor and an Unknown Length
Baseball/Softball Diamond Problem Revisited
All of the corresponding angles are congruent because the shapes are rectangles.
All the sides are in the same ratio. Pick the two largest (or smallest) sides to find the ratio.
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.
△BIG∼△HAT. List the congruent angles and proportions for the sides.
BI=9and HA=15, find the scale factor.
BG=21, find HT.
AT=45, find IG.
- Find the perimeter of
△BIGand △HAT. What is the ratio of the perimeters?
Use the picture to the right to answer questions 14-18.
m∠Eand m∠Q. ABCDE∼QLMNP, find the scale factor.
Determine if the following triangles and quadrilaterals are similar. If they are, write the similarity statement.
△ABC∼△DEF Solve for xand y. QUAD∼KENT Find the perimeter of QUAD. △CAT∼△DOG Solve for xand y. PENTA∼FIVER Solve for x. △MNO∼△XNY Solve for aand b.
HAVE∼KNOTSolve for xand y.
- Two similar octagons have a scale factor of
911. If the perimeter of the smaller octagon is 99 meters, what is the perimeter of the larger octagon?
- Two right triangles are similar. The legs of one of the triangles are 5 and 12. The second right triangle has a hypotenuse of length 39. What is the scale factor between the two triangles?
- What is the area of the smaller triangle in problem 30? What is the area of the larger triangle in problem 30? What is the ratio of the areas? How does it compare to the ratio of the lengths (or scale factor)? Recall that the area of a triangle is
To view the Review answers, open this PDF file and look for section 7.3.