Must show all work (including ratios, proportions, cross-products, etc…) to... 1. Use the diagram to complete the statement.

Similarity and Pythagorean Theorem Test EXTRA Assignment
RHS-Niven
PreAP Geometry
Must show all work (including ratios, proportions, cross-products, etc…) to receive full credit.
1. Use the diagram to complete the statement.
2. Determine whether 𝛥𝐴𝐵𝐶 and 𝛥𝐷𝐸𝐹are similar, not similar or cannot be determined from the information given
in the figure.
3. Determine whether the triangles can be proved similar. If they are similar, write a similarity statement. Explain
your reasoning.
4. Determine which two of the three triangles are similar. Find the scale factor for the pair.
5. Is there enough information to determine whether the triangles are similar? If so, write a similarity statement, find
the scale factor, and write the theorem that justifies your answer.
6.
Similarity and Pythagorean Theorem Test EXTRA Assignment
RHS-Niven
PreAP Geometry
7. Determine the geometric mean of the two values.
a.) 14 and 21
b.) 15 and 20
c.) 18 and 25
8.
9.
11.
10.
12.
13.
Similarity and Pythagorean Theorem Test EXTRA Assignment
RHS-Niven
PreAP Geometry
14. Given similar polygons XCVB and ASDF, complete the statements below.
𝑉𝑋
a.)
𝐷𝐴
=
𝐴𝐹
b.) ∡ 𝐵𝑋𝑉 ≅ ∡_________
15. Solve for AB
𝐷𝐹
c.)
𝐹𝑆
=
𝑉𝐵
16. Solve for AB.
17. Determine is the given side lengths will form a right, acute, or obtuse triangle.
a.) 9, 11, and √115
b.) 10, 16, and 2√39
c.) √247, 4√7 𝑎𝑛𝑑 3√15
18. The given lengths are two sides of a right triangle.
The three side lengths form a Pythagorean Triple.
Determine if the missing side is a leg or hypotenuse
and give its length.
19. The given lengths are two sides of a right triangle.
The three side lengths form a Pythagorean Triple.
Determine if the missing side is a leg or hypotenuse
and give its length.
48 and 55
72 and 75
20. The longer diagonal of a rhombus is 48in. Determine
the length of the shorter diagonal if the perimeter of
the rhombus is 104in.
21. The angles of a triangle are in the extended
ratio of 3:5:8.