Download 7-3 Guided Notes

NAME _____________________________________________ DATE ____________________________ PERIOD _____________
7-3 Guided Notes – FIRST, READ Pgs. 470-473
Similar Triangles
Identify Similar Triangles Here are three ways to show that two triangles are similar. READ pages 470 & 471, then
fill in the blank boxes below.
Postulate/ Theorem
Definition
Sketch an Example
Angle-Angle (AA)
Similarity Postulate
Side-Side-Side (SSS)
Similarity Theorem
Side-Angle-Side (SAS)
Similarity Theorem
Verifying/ Deciding if two triangles are similar STEPS:
Example 1 : Determine whether the triangles
Step 1 : Look for congruent angles! If you have two, you can
use AA Similarity.
are similar.
Step 2: Check to see if the sides are proportional! Do the
ratios match? If so, you might be able to use SSS Similarity
or SAS Similarity (if you also have an included angle)
Step 1: I can see that there aren’t any given congruent
angles.
Step 3: If you are able to verify similarity using one of the
three similarity theorems above, then write your similarity
statement.
Step 2: Next, I need to test the ratios of the sides …
AB 10 2 AC
6 2 CB
8
2

 ;
  ;


DE 15 3 DF
9 3 FE 12 3
Step 3: Since all sides are proportional, I can use SSS
theorem to prove they are similar.
ABC ~ DEF ; SSS
Example 2 : Determine whether the triangles
You Try One… (After you read through the steps and look at examples 1 & 2)
Determine whether the triangles above are similar. If so,
write a similarity statement.
Step 1: Do you see any congruent angles? _____________
Step 2: Do you see any proportional sides? ______________
Step 3: Are you able to use the information above to prove the
triangles
Chapter are
7 similar (using one of the postulates)?
18
Write your similarity statement here: ______________________
are similar.
Step 1: Angles N and R are congruent.
Step 2: Next, I need to test the sides…
MN
3 NP 6 3
 ;
 
QR
4 RS
8 4
Step 3: Since two sides are proportional and their included
angles are congruent, they are similar by SAS
MNP ~ QRS ; SAS
Glencoe Geometry
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
7-3 Guided Notes (continued)
Similar Triangles
Use Similar Triangles Similar triangles can be used to find measurements.
Example1 : △ABC ∼ △DEF. Find the values of x and y. Example 2 : A person 6 feet tall casts a 1.5-foot-long
shadow at the same time that a flagpole casts a 7-footlong shadow. How tall is the flagpole?
Step 1: Set up a ratio using corresponding sides to solve for
y 18
a missing side:

18
9
Step 1: Set up a ratio using corresponding sides to solve for a
6 1 .5
missing side:

x 7
Step 2: Solve for the missing side.
6 1.5

(cross multiply) 1.5x  42 (divide by 1.5) x  48
x
7
Step 2: Solve for the missing side.
y 18

(cross multiply)
18 9
9 y  324 (divide by 9) y  36
Step 3: If necessary, solve for additional missing sides.
18 3 18

x
9
18x  162 3
x9 3
Step 3: If necessary, solve for additional missing sides.
No additional sides to solve for. So, the flagpole is 48 ft tall
You Try One… (After you read through the steps and look at examples 1 & 2)
It is given that these triangles are similar. Now, solve for the
missing side.
When you have finished reading ALL
examples, then begin:
Step 1: Set up a ratio using the corresponding sides:
Assignment #14
Pg. 474
#1-6
_____________
Step 2: Solve the ratio:
______________
Step 3: Are there any more variables to solve for?
Chapter 7
19
Glencoe Geometry