Similar Triangles Color by Number - Free Printable

The image you uploaded shows a "Color by Number" activity focused on Similar Triangles. The task involves solving problems related to similar triangles and then using the answers to color a picture according to a provided key. Below, I will explain how to solve the problems and use the results for coloring.

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Step 1: Understand Similar Triangles

Two triangles are similar if:
1. Their corresponding angles are equal.
2. Their corresponding sides are proportional.

If two triangles are similar, the ratio of their corresponding side lengths is constant. This ratio is called the scale factor.

For example, if ΔABC ~ ΔDEF, then:
\[
\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}
\]

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Step 2: Solve the Problems

The left sheet contains four problems involving similar triangles. Each problem provides two similar triangles and asks you to find a missing side length or value. Let's solve each one step by step.

#### Problem 1: ΔMLK ~ ΔQRP
- Given: \( ML = 10 \), \( QR = 8 \), \( MK = 12 \)
- Find: \( RP \)

Since the triangles are similar, the ratios of corresponding sides are equal:
\[
\frac{ML}{QR} = \frac{MK}{RP}
\]
Substitute the given values:
\[
\frac{10}{8} = \frac{12}{RP}
\]
Simplify the ratio \( \frac{10}{8} \):
\[
\frac{5}{4} = \frac{12}{RP}
\]
Cross-multiply to solve for \( RP \):
\[
5 \cdot RP = 4 \cdot 12
\]
\[
5 \cdot RP = 48
\]
\[
RP = \frac{48}{5} = 9.6
\]

So, the answer for Problem 1 is \( 9.6 \).

#### Problem 2: ΔEFG ~ ΔLQP
- Given: \( EF = 36 \), \( LQ = 24 \), \( FG = x \), \( QP = 18 \)
- Find: \( x \)

Using the similarity ratio:
\[
\frac{EF}{LQ} = \frac{FG}{QP}
\]
Substitute the given values:
\[
\frac{36}{24} = \frac{x}{18}
\]
Simplify the ratio \( \frac{36}{24} \):
\[
\frac{3}{2} = \frac{x}{18}
\]
Cross-multiply to solve for \( x \):
\[
3 \cdot 18 = 2 \cdot x
\]
\[
54 = 2x
\]
\[
x = \frac{54}{2} = 27
\]

So, the answer for Problem 2 is \( 27 \).

#### Problem 3: ΔCDE ~ ΔUTS
- Given: \( CD = 48 \), \( UT = 32 \), \( DE = 18 \), \( TS = x \)
- Find: \( x \)

Using the similarity ratio:
\[
\frac{CD}{UT} = \frac{DE}{TS}
\]
Substitute the given values:
\[
\frac{48}{32} = \frac{18}{x}
\]
Simplify the ratio \( \frac{48}{32} \):
\[
\frac{3}{2} = \frac{18}{x}
\]
Cross-multiply to solve for \( x \):
\[
3 \cdot x = 2 \cdot 18
\]
\[
3x = 36
\]
\[
x = \frac{36}{3} = 12
\]

So, the answer for Problem 3 is \( 12 \).

#### Problem 4: ΔBFA ~ ΔGPE
- Given: \( BF = 18 \), \( GP = 12 \), \( FA = 24 \), \( PE = x \)
- Find: \( x \)

Using the similarity ratio:
\[
\frac{BF}{GP} = \frac{FA}{PE}
\]
Substitute the given values:
\[
\frac{18}{12} = \frac{24}{x}
\]
Simplify the ratio \( \frac{18}{12} \):
\[
\frac{3}{2} = \frac{24}{x}
\]
Cross-multiply to solve for \( x \):
\[
3 \cdot x = 2 \cdot 24
\]
\[
3x = 48
\]
\[
x = \frac{48}{3} = 16
\]

So, the answer for Problem 4 is \( 16 \).

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Step 3: Use the Answers to Color the Picture

The middle sheet shows a color key with numbers corresponding to colors. Use the answers from the problems to determine which sections of the circular design to color.

- Problem 1: \( 9.6 \) → Find the section labeled \( 9.6 \) and color it according to the key.
- Problem 2: \( 27 \) → Find the section labeled \( 27 \) and color it according to the key.
- Problem 3: \( 12 \) → Find the section labeled \( 12 \) and color it according to the key.
- Problem 4: \( 16 \) → Find the section labeled \( 16 \) and color it according to the key.

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Final Answer

The solutions to the problems are:
1. \( 9.6 \)
2. \( 27 \)
3. \( 12 \)
4. \( 16 \)

Use these values to color the corresponding sections in the circular design. The final colored image should match the example shown on the right.

\[
\boxed{9.6, 27, 12, 16}
\]