Review: Unit 4.8 – 4.11
Unit 4.8 Triangle Inequalities
List the angles of each triangle from smallest to largest.
1)
2)
3)
State whether it is possible to have a triangle with the following side lengths:
5) 3 inches, 5 inches, and 8 inches
6) 2 meters, 4 meters, and 3 meters
7) 1.5 feet, 3 feet, 4.5 feet
8) 3 feet, 4 feet, 24 inches
9) 7 meters, 8 meters, 1 meter
10) 9 miles, 10 miles, 11 miles
11) 6.5 feet, 27 feet, 30 feet
12) 1 meter, 3 meters, 250 centimeters
Find the range of possible lengths for the third side of each triangle listed below:
13) 4 feet and 6 feet
14) 2 meters and 1 meter
15) 1 unit and 5 units
4)
Unit 4.9 Similarity in Triangles
List the corresponding sides of each pair of triangles below. Then determine whether the triangles are
similar. If they are similar, write a similarity statement and say why they are similar. If not, write not similar.
Corresponding Sides:
Smallest
Medium
Largest
Side Names:
Side Lengths:
16) Similar or Not Similar: __________
Similarity Statement: _________________________________
Corresponding Sides:
Smallest
Medium
Largest
Side Names:
Side Lengths:
17) Similar or Not Similar: __________
Similarity Statement: _________________________________
Corresponding Sides:
Smallest
Medium
Largest
Side Names:
Side Lengths:
18) Similar or Not Similar: __________
Similarity Statement: _________________________________
Corresponding Sides:
Smallest
Medium
Side Names:
Side Lengths:
19) Similar or Not Similar: __________
Similarity Statement: _________________________________
Largest
20) Complete the following proof to show that JHK ~ MHL
Statements
Reasons
𝐽𝐾||𝐿𝑀
< 𝐽𝐾𝐻 ≅ < 𝐻𝐿𝑀
< 𝐾𝐽𝐻 ≅ < 𝐻𝑀𝐿
21) Complete the following proof to show that LNM ~ PNO
Statements
Reasons
< 𝐿𝑁𝑀 ≅ < 𝑂𝑁𝑃
𝑇𝑕𝑒 𝑙𝑒𝑔𝑠 𝑜𝑛 𝑒𝑖𝑡𝑕𝑒𝑟 𝑠𝑖𝑑𝑒 𝑜𝑓
< 𝑁 𝑎𝑟𝑒 𝑝𝑟𝑜𝑝𝑜𝑟𝑡𝑖𝑜𝑛𝑎𝑙
Each pair of triangles below is similar. List the corresponding sides for each pair, then find x.
Corresponding Sides:
Smallest
Medium
Largest
Side Names:
Side Lengths:
22) x = __________
Similarity Statement: _______________________________________________________
Corresponding Sides:
Smallest
Medium
Side Names:
Side Lengths:
23) x = __________
Similarity Statement: _______________________________________________________
Largest
4.10 Similarity in Right Triangles
For each right triangle cut into smaller right triangles by an altitude: Fill in the corresponding sides for all
three triangles from smallest side of the smallest triangle to largest side of the largest triangle. Then solve
for x and y using proportions and write a similarity statement.
Corresponding Sides:
Smallest
Medium
Largest
Side Names:
Side Lengths:
24)
x = __________
y =__________
Similarity Statement: ________________________________________________
Corresponding Sides:
Smallest
Medium
Largest
Side Names:
Side Lengths:
25)
x = __________
y =__________
Similarity Statement: ________________________________________________
Corresponding Sides:
Smallest
Medium
Largest
Side Names:
26)
x = __________
Side Lengths:
Similarity Statement: ________________________________________________
4.11 Proportions in Triangles
Solve for x in each figure below.
31)
27)
32)
28)
33)
29)
34)
30)
Miscellaneous Review: Midsegments
Solve for x.
35)
36)
37)
Miscellaneous Review: Medians
In the following triangle, Y is the centroid.
38) If XY is 9, find YV and XV.
41) If UY is 16, find UZ and YZ.
39) If TW is 9, find TY and YW.
42) If YV is 10, find XY and XV.
40) If YZ is 12, find UY and UZ.
43) If UZ is 21, find UY and YZ.