1. 2.5 Similar Figures
Essential Question: How can you determine if two figures are similar or not?
Trapezoids ABCD and EFGH are congruent.
Congruent: (same corresponding side lengths & angles)
Review on Congruent Figures:
1. Which side of EFGH is corresponds to side AD?
2. The perimeter of ABCD is 30 centimeters. What is the value of x?
3. What is the length of side EF?
4. What is the length of side GF?

2. SIMILAR FIGURE REQUIREMENTS
Two figures are similar if:
1. The measures of their corresponding angles are equal.
2. The ratios of the lengths of the corresponding sides are proportional.
(same shape but not necessarily same size)
The symbol ~ a “tilde” means “is similar to.”
SIMILAR FIGURE REQUIREMENTS

3. SIMILAR FIGURES Big 𝑇𝑟𝑖𝑎𝑛𝑔𝑙𝑒 𝑆𝑚𝑎𝑙𝑙 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒
𝑆𝑚𝑎𝑙𝑙 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒 𝐵𝑖𝑔 𝑇𝑟𝑖𝑎𝑛𝑔𝑙𝑒 =

4. Example 1- Are Two Triangles Similar?
Identify the corresponding sides in the pair of triangles. Then use ratios to determine whether the triangles are similar. E
AB corresponds to DE.
16 in
10 in A C
28 in
BC corresponds to EF.
4 in D
7 in
40 in F
AC corresponds to DF. B AB DE = ? BC EF = ? AC DF
Write ratios using the corresponding sides. 4 16 = ? 7 28 = ? 10 40
Substitute the length of the sides. 1 4 = ? 1 4 = ? 1 4
Simplify each ratio.
Since the ratios of the corresponding sides are equivalent, the triangles are similar.

5. Example 2- Find missing side of similar figures

6. Example 3: Indirect Measurement
The inside triangle is similar in shape to the outside triangle.
Find the height of the outside triangle. 8 h 14 30 =
Write a proportion. 8 h 14 30
Use compatible numbers to estimate. =
Simplify.
8 • 30 = 14 • h
Cross multiply.
240 = 14h
Divide each side by 3 to isolate the variable.
17 ≈ h
The outside triangle is about 17 feet tall.

7. White Boards

8. textbook 2.5 pg 74 #1, 2, 4, 8, 9, 10, 11, 13, 17, 18, (19 bonus)