Key Concepts

Key Concepts

• Problem-Solving Strategy for Geometry Applications
  
  1. Read the problem and make all the words and ideas are understood. Draw the figure and label it with the given information.
  2. Identify what we are looking for.
  3. Name what we are looking for by choosing a variable to represent it.
  4. Translate into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.
  5. Solve the equation using good algebra techniques.
  6. Check the answer in the problem and make sure it makes sense.
  7. Answer the question with a complete sentence.
• Triangle Properties For \(\text{△}ABC\)
  Angle measures:
  • \(m\text{∠}A+m\text{∠}B+m\text{∠}C=180\)
  Perimeter:
  • \(P=a+b+c\)
  Area:
  • \(A=\frac{1}{2}bh,\phantom{\rule{0.2em}{0ex}}\text{b}=\text{base},\text{h}=\text{height}\)
  A right triangle has one \(90\text{°}\) angle.
• The Pythagorean Theorem In any right triangle, \({a}^{2}+{b}^{2}={c}^{2}\) where c is the length of the hypotenuse and a and b are the lengths of the legs.
• Properties of Rectangles
  
  • Rectangles have four sides and four right (90°) angles.
  • The lengths of opposite sides are equal.
  • The perimeter of a rectangle is the sum of twice the length and twice the width: \(P=2L+2W.\) The area of a rectangle is the length times the width: \(A=LW.\)