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Notes

Practice Problems

Solve for the variables.

\(\textbf{1)}\) Solve for x

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\(\text{The answer is } x=6 \)

Show Work

\(\,\,\,\,\,\,e^2=c \cdot d\)

\(\,\,\,\,\,\,x^2=9 \cdot 4\)

\(\,\,\,\,\,\,x^2=36\)

\(\,\,\,\,\,\,x=6\)

\(\,\,\,\,\,\, \text{The answer is } x=6 \)

\(\textbf{2)}\) Solve for y

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The answer is \( y=2\sqrt{13} \)

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\(\,\,\,\,\,\,b^2=d \cdot (c+d)\)

\(\,\,\,\,\,\,y^2=4 \cdot (4+9)\)

\(\,\,\,\,\,\,y^2=4 \cdot 13\)

\(\,\,\,\,\,\,y^2=52\)

\(\,\,\,\,\,\,\sqrt{y^2}=\sqrt{52}\)

\(\,\,\,\,\,\,y=2\sqrt{13}\)

\(\textbf{3)}\) Solve for z

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The answer is \( z=3\sqrt{13} \)

\(\textbf{4)}\) Solve for x

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The answer is \( x=4 \)

Show Work

\(\,\,\,\,\,\,e^2=c \cdot d\)

\(\,\,\,\,\,\,x^2=8 \cdot 2\)

\(\,\,\,\,\,\,x^2=16\)

\(\,\,\,\,\,\,x=4\)

\(\,\,\,\,\,\, \text{The answer is } x=4 \)

\(\textbf{5)}\) Solve for y

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The answer is \( y=2\sqrt{5} \)

Show Work

\(\,\,\,\,\,\,b^2=d \cdot (c+d)\)

\(\,\,\,\,\,\,y^2=2 \cdot (2+8)\)

\(\,\,\,\,\,\,y^2=2 \cdot 10\)

\(\,\,\,\,\,\,y^2=22\)

\(\,\,\,\,\,\,\sqrt{y^2}=\sqrt{20}\)

\(\,\,\,\,\,\,y=2\sqrt{5}\)

\(\textbf{6)}\) Solve for z

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The answer is \( z=4\sqrt{5} \)

\(\textbf{7)}\) Solve for x

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The answer is \( x=3 \)

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\(\,\,\,\,\,\,e^2=c \cdot d\)

\(\,\,\,\,\,\,9^2=27 \cdot x\)

\(\,\,\,\,\,\,81=27 \cdot x\)

\(\,\,\,\,\,\,3=x\)

\(\textbf{8)}\) Solve for z

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The answer is \( z=25 \)

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\(\,\,\,\,\,\,e^2=c \cdot d\)

\(\,\,\,\,\,\,10^2=z \cdot 4\)

\(\,\,\,\,\,\,100=4z\)

\(\,\,\,\,\,\,25=z \cdot x\)

\(\textbf{9)}\) Solve for x, y, and z

Show x

The answer is \( x=4\sqrt{3} \)

Show y

The answer is \( y=8 \)

Show z

The answer is \( z=8\sqrt{3} \)

\(\textbf{10)}\) Solve for x

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The answer is \( x=6\sqrt{2} \)

\(\textbf{11)}\) Solve for y

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The answer is \( y=2\sqrt{22} \)

\(\textbf{12)}\) Solve for z

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The answer is \( z=2\sqrt{143} \)

\(\textbf{13)}\) Solve for x

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The answer is \( x=20 \)

\(\textbf{14)}\) Solve for z

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The answer is \( z=2\sqrt{30} \)

Challenge Problems

\(\textbf{15)}\) Solve for w, z, and x

Show w

The answer is \( w=50 \)

Show z

The answer is \( z=4\sqrt{29} \)

Show x

The answer is \( x=10\sqrt{29} \)

\(\textbf{16)}\) Solve for x and z

Show x

The answer is \( x=6 \)

Show z

The answer is \( z=6\sqrt{5} \)

\(\textbf{17)}\) Solve for x

Show Answer

The answer is \( x=9 \)

\(\textbf{18)}\) Write the triangle similarity statement for all 3 triangles below.

Show Answer

The answer is \( \bigtriangleup ANY \sim \bigtriangleup YND \sim \bigtriangleup AYD \)
(Other answers may be correct as long as the angles line up correctly)

See Related Pages\(\)

\(\bullet\text{ Geometry Homepage}\)
\(\,\,\,\,\,\,\,\,\text{All the Best Topics…}\)

\(\bullet\text{ SideSplitter Theorem}\)
\(\,\,\,\,\,\,\,\,\)

\(\bullet\text{ Geometric Mean}\)
\(\,\,\,\,\,\,\,\,\)

In Summary

Similar triangles have congruent corresponding angles, and proportional corresponding side lengths. Similar right triangles can be created when you drop an altitude from the right angle of a right triangle. This is typically studied in a high school geometry course. The geometric mean is usually introduced in this context.

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