Acute, Obtuse or Right?

Acute, Obtuse or Right?

Using the Pythagorean Theorem to classify triangles.

Acute, Obtuse or Right?

•  $a^2+b^2=c^2\ \ \ RIGHT\ TRIANGLE$  

•  $a^2+b^2<c^2\ \ \ OBTUSE\ TRIANGLE$  

•  $a^2+b^2>c^2\ \ \ ACUTE\ TRIANGLE$  

Multiple Choice

Please classify the triangle with sides 4, 11 and 9.

• Acute

• Obtuse

• Right

Multiple Choice

Please classify the triangle with sides 43, 43, 43

• Acute

• Obtuse

• Right

Multiple Choice

Please classify the triangle with sides 12, 9 and 4

• Acute

• Obtuse

• Right

Multiple Choice

Please classify the triangle with sides

 $4,\ 2\sqrt{15},\ 6$  

• Acute

• Obtuse

• Right

 $4,\ 2\sqrt{15},\ 6$  

• What is the longest side?     

•  $2\sqrt{15}=7.74$  so it is the longest side

•  $4^2=16$   $6^2=36$  

•  $\left(2\sqrt{15}\right)^2=2^2\times\left(\sqrt{15}\right)^2=4\times15=60$  

•  $52<60\ \ \ so\ it's\ OBTUSE$  

Multiple Choice

Please classify the triangle with sides

 $\sqrt{13},\ \sqrt{5},\ \sqrt{12}$  

• Acute

• Obtuse

• Right

Multiple Choice

Please classify the triangle with sides

 $\sqrt{13},\ \sqrt{5},\ \sqrt{8}$  

• Acute

• Obtuse

• Right

Multiple Choice

Please classify the triangle with sides

 $\frac{\sqrt{3}}{5},\ \frac{\sqrt{6}}{5},\ \frac{3}{5}$  

• Acute

• Obtuse

• Right

 $\frac{\sqrt{3}}{5},\ \frac{\sqrt{6}}{5},\ \frac{3}{5}$  is a right triangle?

•  $\left(\frac{\sqrt{3}}{5}\right)^2=\frac{\left(\sqrt{3}\right)^2}{5^2}=\frac{3}{25}$  

•  $\left(\frac{\sqrt{6}}{5}\right)^2=\frac{\left(\sqrt{6}\right)^2}{5^2}=\frac{6}{25}$  

•  $\left(\frac{3}{5}\right)^2=\frac{9}{25}$