1. HW, red pen, pencil, GP NB, highlighter, & calculator
U8D10
HW, red pen, pencil, GP NB, highlighter, & calculator
Have Out:
The ratio of the volumes of two similar triangular prisms is 27: Calculate the following:
Bellwork:
Ratio of similarity:
Side ratio:
r:r2:r3 Thm. +1
Vr = r3
(r:r2:r3 Thm.)
Perimeter ratio:
r:r2:r3 Thm.
r3 =
Area ratio:
r:r2:r3 Thm. +1

2. The ratio of the areas of two similar polygons is 16:81.
a) What is the ratio of similarity for the polygons?
Ar = r2
r:r2:r3 Thm.
b) If the perimeter of the smaller polygon is 112, what is the perimeter of the larger polygon?
112 P = 4 9
4P = 9(112)
The perimeter of the larger polygon is 252 units.
r:r2:r3 Thm.
9(112)
P = 4
P = 252 u

3. These triangles are not similar. Therefore . . .
In the triangles at right, both have one 80 angle.
a) Since B  B’, does this alone guarantee that ABC  A’B’C’? Explain. A B C
80 A B C
These triangles are not similar. Therefore . . .
80
No! ONE PAIR of congruent angles does NOT guarantee similar triangles We need 2 pairs of congruent angles. B’ A’ C’
80 A’ A
80 C’ B’ B C
Skip the rest of S-95.

4. a) Are triangles WHS and W’H’S’ similar? Explain.
Suppose WHS has side lengths of WH = 3cm, HS = 4 cm, and WS = 6cm. What would be the sides of W′H′S′ with sides twice as long in WHS ?
W’H’ = 6 cm
H’S’ = 8 cm
W’S’ = 12 cm
a) Are triangles WHS and W’H’S’ similar? Explain. W H S
3cm
4cm
6cm W′ H′ S′
6cm
8cm
12cm
Yes they are  because each pair of corresponding sides have a side ratio of 1 2
Skip the rest of S-96.
(The 2nd triangle is a magnification of the 1st triangle.)

5. There are other ways to prove similarity in triangles.
Add to your notes
SAS ~ Theorem
If you have two pairs of corresponding sides proportional and the included angles are congruent, then the triangles are similar. 4 10 6 15
If one triangle is a magnification of the other, so all pairs of corresponding sides are proportional, then the two triangles are similar.
SSS ~ Theorem 12 6 3 6
Notice: the sides need to be proportional, not congruent, for similarity. 4 8

6. Recall the congruence properties from Unit 5: SSS, SAS, ASA, and HL
a) Do we need an ASA Theorem for similarity? Explain.
No, AA alone is enough to prove similarity.
b) How is SAS ~ Theorem different from SAS for congruency?
For SAS ~ the sides are only proportional to show similarity. They must be equal to show congruence by SAS.
c) How is SSS ~ Theorem different from SSS for congruency?
For SSS ~ the sides are only proportional to show similarity. They must be equal to show congruence by SSS.

7. Are these two triangles similar? Explain why or why not.4’ 6’ 6’ 8’ X′ Z′ X Z =
X′Y′ XY = 4 6 = 2 3 Sr
The sides are not proportional! Therefore the s are not similar. =
Y′Z′ YZ = 6 8 = 3 4
YZ would have to be 9’. Sr

8. Finish the assignment...
S &
Similarity Worksheet
Study for the
Test on Tuesday!