Summary: Using the Properties of Angles, Triangles, and the Pythagorean Theorem
Key Concepts
- Supplementary and Complementary Angles
- If the sum of the measures of two angles is 180°, then the angles are supplementary.
- If angle [latex]A[/latex] and angle [latex]B[/latex] are supplementary, then [latex]m\angle{A}+m\angle{B}=180°[/latex] .
- If the sum of the measures of two angles is [latex]90^\circ[/latex], then the angles are complementary.
- If angle [latex]A[/latex] and angle [latex]B[/latex] are complementary, then [latex]m\angle{A}+m\angle{B}=90°[/latex] .
- Solve Geometry Applications
- Read the problem and make sure you understand all the words and ideas. Draw a figure and label it with the given information.
- Identify what you are looking for.
- Name what you are looking for and choose a variable to represent it.
- Translate into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.
- Solve the equation using good algebra techniques.
- Check the answer in the problem and make sure it makes sense.
- Answer the question with a complete sentence.
- Sum of the Measures of the Angles of a Triangle
- For any [latex]\Delta ABC[/latex], the sum of the measures is [latex]180^\circ[/latex]
- [latex]m\angle{A}+m\angle{B}=180°[/latex]
- Right Triangle
- A right triangle is a triangle that has one [latex]90°[/latex] angle, which is often marked with a [latex]\angle[/latex] symbol.
- Properties of Similar Triangles
- If two triangles are similar, then their corresponding angle measures are equal and their corresponding side lengths have the same ratio.
Glossary
- angle
- An angle is formed by two rays that share a common endpoint. Each ray is called a side of the angle.
- complementary angles
- If the sum of the measures of two angles is [latex]90^\circ [/latex] , then they are called complementary angles.
- hypotenuse
- The side of the triangle opposite the [latex]90^\circ[/latex] angle is called the hypotenuse.
- legs of a right triangle
- The sides of a right triangle adjacent to the right angle are called the legs.
- right triangle
- A right triangle is a triangle that has one [latex]90^\circ [/latex] angle.
- similar figures
- In geometry, if two figures have exactly the same shape but different sizes, we say they are similar figures.
- supplementary angles
- If the sum of the measures of two angles is [latex]180^\circ [/latex] , then they are called supplementary angles.
- triangle
- A triangle is a geometric figure with three sides and three angles.
- vertex of an angle
- When two rays meet to form an angle, the common endpoint is called the vertex of the angle.
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