Angles and Proofs Review Notes

General Review Instructions

• Assessment includes both review sheet and additional materials like PPTs and IXLs.

• Focus on proofs covered; at least one proof will be on the test.

• Review angles related to parallel lines; ensure ability to solve and provide answers.

Angles in Parallel Lines

• Questions 5-7 ask about corresponding angles and proving parallel lines:

  • Question 5: Identify corresponding angles.

  • Question 6: Determine what information proves lines are parallel.

  • Question 7: Given if line 1 is parallel to line m and angle measures, calculate values.

Angles in Triangles

• Work with angles in triangles and exterior angles:

  • Example to solve for x based on given angle expressions.

• Specific triangles:

  • Use expressions for angles like $(8x + 2)^ ext{o}$, $(16x - 7)^ ext{o}$, $(10x - 19)^ ext{o}$, etc., to solve for x and find measurements.

Parallelogram Angles

• Task: Find measurements in given parallelograms using angle properties:

  • Understand relationships between angles (e.g., opposite angles are equal, consecutive angles are supplementary).

• Solve equations involving expressions for the angles to find $x$.

Interior and Exterior Angles

• Find missing angles in polygons:

  • Calculate using the sum of interior angles formula: (n-2) imes 180^ ext{o} where n is the number of sides.

• Work with quadrilaterals and identify missing angles using their properties.

Regular Polygons

• Calculate interior and exterior angles:

  • Label polygon interior/exterior angle formulas.

• For varying side counts, calculate angle sizes and explain impossibilities for given degree measures of angles.

Similarity in Triangles

• Understand triangle similarity conditions:

  • Apply AA (Angle-Angle) criterion, SSS (Side-Side-Side), or SAS (Side-Angle-Side).

  • Materials include pairs of triangles to analyze and prove similarity.

Proofs

• Write proofs in two-column format:

  • Include statements such as "Given: p || q" and corresponding reasons (e.g., properties of parallel lines).