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Geometry – 3.3 – Using Ratios of Similarity
Name
Pd.
1. Given that ∆𝐴𝐹𝐺~∆𝐷𝑅𝐻. Complete the following.
𝐷𝑅
=
𝐴𝐹
∠𝐻 ≅ ________
𝐷𝐻
∠𝐷 ≅ ________
=
𝑅𝐻
𝟐. ∆𝐴𝐵𝐶 is similar to another ∆. Provided is information about the two ∆s,
𝐴𝐺
𝐷𝐻
𝐵𝐶 𝐴𝐵
=
.
𝐷𝑅 𝑇𝐷
From this information, determine the ∆ similarity statement: ∆𝐴𝐵𝐶~∆______________
The two figures in each problem are similar. Create a similarity statement from the diagram.
3. TRYON ~ _______________________
R
4. ∆MAX ~ _______________________
5. ∆BAC ~ _______________________
B
C
T
N
Y
A
A
Y
B
C
O
Z
I
D
E
List all pairs of congruent angles for the figures. Then write the ratios of the corresponding sides
in a statement of proportionality.
6. DEFG ~ PQRS
Angles:
Sides:
7. ∆𝐴𝐵𝐶~∆𝐷𝐸𝐹. Which statement is NOT correct?
A.
𝐵𝐶 𝐴𝐶
=
𝐸𝐹 𝐷𝐹
B.
𝐴𝐵 𝐶𝐴
=
𝐷𝐸 𝐹𝐷
C.
𝐶𝐴 𝐵𝐶
=
𝐹𝐷 𝐸𝐹
D.
𝐴𝐵 𝐵𝐶
=
𝐸𝐹 𝐷𝐸
Determine whether the triangles are similar by comparing angles and sides. If the ∆s are similar,
write a similarity statement and find the scale factor.
8.
Angles:
Sides:
Similarity Statement: ∆________________ ~∆________________
Scale Factor: ____________
For #9-#11, use the diagram at the right showing JKLM~EFGH.
9. Find the scale factor of JKLM to EFGH.
10. Find the values of x, y, and z. Show work!
11. Find the perimeter of each polygon.
12. Two similar FOR SALE signs have a scale factor of 5:3. The large sign’s perimter is 60 inches.
Find the small sign’s perimeter.
Determine the sequence of similarity transformations that map one figure onto the other thus
establishing that the two figures are similar. Be specific. (for example, translation up 4 units,
reflection over the x-axis, 90˚ rotation clockwise, dilation using a scale factor of 3, etc.)
13. Determine two similarity transformations that would map ABCD to ALMN.
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14. Determine two similarity transformations that would map ∆ABC to ∆AML.
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