You used proportions to solve problems.
• Use proportions to identify similar polygons.
• Solve problems using the properties of similar polygons.
• similar polygons
• scale factor
Use a Similarity Statement
If ΔABC ~ ΔRST, list all pairs of congruent angles and write a proportion that relates the corresponding sides.
Use a Similarity Statement
Use the similarity statement.
ΔABC ~ ΔRST
Congruent Angles: A R, B S, C T
Answer:
If ΔGHK ~ ΔPQR, determine which of the following similarity statements is not true.
A. HGK QPR
B.
C. K R
D. GHK QPR
Use Similar Figures to Find Missing Measures
A. The two polygons are similar. Find x.
Use the congruent angles to write the corresponding vertices in order.
polygon ABCDE ~ polygon RSTUV
Use Similar Figures to Find Missing Measures
Write a proportion to find x.
Similarity proportion
Cross Products Property
Multiply.
Divide each side by 4. Simplify.
Answer: x = __92
Use Similar Figures to Find Missing Measures
B. The two polygons are similar. Find y.
Use the congruent angles to write the corresponding vertices in order.
polygon ABCDE ~ polygon RSTUV
Use Similar Figures to Find Missing Measures
Similarity proportion
Cross Products Property
Multiply.
Subtract 6 from each side.
Divide each side by 6 and simplify.
AB = 6, RS = 4, DE = 8, UV = y + 1
Answer: y = __313
A. a = 1.4
B. a = 3.75
C. a = 2.4
D. a = 2
A. The two polygons are similar. Solve for a.
A. 1.2
B. 2.1
C. 7.2
D. 9.3
B. The two polygons are similar. Solve for b.
Use a Scale Factor to Find Perimeter
If ABCDE ~ RSTUV, find the scale factor of ABCDE to RSTUV and the perimeter of each polygon.
Use a Scale Factor to Find Perimeter
The scale factor ABCDE to RSTUV is or . ___AEVU
__47
Write a proportion to find the length of DC.
Since DC AB and AE DE, the perimeter of ABCDE is 6 + 6 + 6 + 4 + 4 or 26.
Write a proportion.
4(10.5)= 7 ● DC Cross Products Property
6 = DC Divide each side by 7.
Use a Scale Factor to Find Perimeter
Use the perimeter of ABCDE and scale factor to write a proportion. Let x represent the perimeter of RSTUV.
Theorem 7.1
Substitution
4x = (26)(7) Cross Products Property
x = 45.5 Solve.
Use a Scale Factor to Find Perimeter
Answer: The perimeter of ABCDE is 26 and the perimeter of RSTUV is 45.5.
A. LMNOP = 40, VWXYZ = 30
B. LMNOP = 32, VWXYZ = 24
C. LMNOP = 45, VWXYZ = 40
D. LMNOP = 60, VWXYZ = 45
If LMNOP ~ VWXYZ, find the perimeter of each polygon.