A Similar Triangles Conjecture
Name_________________________________________
Hour___________
C
In the triangles to the right, ∠𝐴 ≅ ∠𝐷 𝑎𝑛𝑑 ∠𝐵 ≅ ∠𝐸.

What is the measure of ∠𝐶 and why?

What is the measure of ∠𝐹 and why?
A
320
D
400
B
F
320
400
Measure the sides and compare the ratios of corresponding side lengths.
𝐴𝐵
𝐴𝐶
𝐵𝐶

Is

Is ∆𝐴𝐵𝐶 ~ ∆𝐷𝐸𝐹 ? Why or why not?
𝐷𝐸
≈
𝐷𝐹
≈
𝐸𝐹
?
Now, draw your own ∆𝐴𝐵𝐶 with different side lengths between 2cm and 5cm long.
Construct a 2nd triangle, ∆𝑋𝑌𝑍, above as well, but with different side lengths of ∆𝐴𝐵𝐶. Make
this triangle not congruent to ∆𝐴𝐵𝐶 but with ∠𝑋 = ∠𝐴 and ∠𝑌 = ∠𝐵. (use a protractor and
ruler to help you)
Are your two triangles ∆𝑨𝑩𝑪 𝒂𝒏𝒅 ∆𝑿𝒀𝒁 similar? Explain.
E
Similarity Practice 2
Name_______________________________
Hour____________
Ready
1. How can you determine if two polygons are similar?
Explain if each statement is true or false. Explain your reasoning.
2. All squares are similar.
3. If an acute angle of a right triangle is congruent to an acute angle of a second right triangle, then the
triangles are similar.
4. All isosceles triangles are similar.
Q
For #5-7, ∆𝑨𝑪𝑩~∆𝑷𝑪𝑸. (See figure on right
6.
Find AQ.
7.
Find AB.
600
5.
10 ft
B
Find 𝑚∠𝑄.
2.5 ft
C
600
A
P
Set
For problems #8-11, ∆𝑨𝑩𝑪~∆𝑿𝒀𝒁. For each problem, sketch and label the given angles or sides for
∆𝑨𝑩𝑪 𝒂𝒏𝒅 ∆𝑿𝒀𝒁. Then solve for t.
8.
𝑚∠𝐴 = 100°
9.
𝐴𝐵 = 8𝑐𝑚
10.
𝐴𝐵 = 𝑡
11.
𝐶𝐵 = 14𝑚
𝑚∠𝐵 = 60°
𝐵𝐶 = 10 𝑐𝑚
𝐴𝐶 = 15 𝑓𝑡
𝐶𝐴 = 5𝑚
𝑚∠𝑍 = 𝑡
𝑋𝑌 = 12𝑐𝑚
𝑋𝑌 = 9𝑓𝑡
𝑍𝑋 = 7𝑚
𝑌𝑍 = 𝑡
𝑋𝑍 = 6 𝑓𝑡
𝑍𝑌 = 𝑡 + 1
12.
13.
Alicia and Jason were writing proportions for similar triangles shown at the right.
Alicia
Jason
𝑟
𝑠
=
𝑘 𝑚
𝑟 𝑚
=
𝑘
𝑠
𝑟𝑚 = 𝑘𝑠
𝑟𝑠 = 𝑘𝑚
r
t
s
k
m
n
\
Who is correct? Explain your reasoning.
Identify the similar triangles (write a similarity statement). Find x and the
measures of the sides AB and DE.
A
E
x
B
3
F
x-4
5
C
D
Go!
15.
To make concrete for the footings of her new deck, Marie mixes cement and sand in a ratio of 2 bags
cement to 3 bags of sand. How many bags of sand will she need if she uses 32 bags of cement?
16.
A 212-pound person weighs about 34 pounds on the moon. About how much will a 130-pound person
weight on the moon?
17.
A baker’s recipe calls for 6 cups of flour for every 2 cups of milk. If the baker uses 9 cups of flour, how
many cups of milk will he need?
18.
A machine worker can produce 75 auto parts in 1.5 hours. How many auto parts can the worker
produce in 5 hours?
19.
A survey shows that four out of every seven students watches TV more than three hours per day. If
there are 560 seniors in a high school, how many would you expect to watch more than three hours of
TV every day?
20.
The advertisement for a scale model of a classic automobile gives the scale of the model as 1 to 24. The
1
model is 7 4 inches long. What is the actual length of the automobile?