Midterm Review Sheet Geo 2025

Geometry Common Core Midterm Review

General Information

• Date: January 24th, 2025

• Time: 8:00 AM

• Name, Period: (To be filled out)

Important Facts and Formulas

• Slope: Represents the steepness of a line. Formula: ( m = \frac{y_2 - y_1}{x_2 - x_1} )

• Relationship Between Perpendicular Lines: The slopes of perpendicular lines are negative reciprocals. If line 1 has a slope of ( m ), then a line perpendicular to it has a slope of ( -\frac{1}{m} ).

• Equation of Line in Slope-Intercept Form: ( y = mx + b )

  • Where: ( m ) is the slope and ( b ) is the y-intercept.

• Relationship Between Parallel Lines: Parallel lines have the same slope.

• Equation of Line in Point-Slope Form: ( y - y_1 = m(x - x_1) )

• Distance Formula: The distance between two points ( (x_1, y_1) ) and ( (x_2, y_2) ) is given by: ( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} )

• Midpoint Formula: The midpoint ( M ) between points ( (x_1, y_1) ) and ( (x_2, y_2) ) is: ( M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) )

• Centroid of a Triangle: The coordinates of the centroid ( G ) can be found using: ( G = \left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right) )

• Complementary Angles: Two angles are complementary if the sum of their measures is 90°.

• Supplementary Angles: Two angles are supplementary if the sum of their measures is 180°.

• Vertical Angles: When two lines intersect, each pair of opposite angles is called vertical angles and they are equal.

• Sum of Interior Angles of a Triangle: The sum is always 180°.

• Exterior Angle of a Triangle: The exterior angle is equal to the sum of the two opposite interior angles.

• Equation of Circle Centered at (h, k): ( (x - h)^2 + (y - k)^2 = r^2 ) where ( r ) is the radius.

Additional Focus Areas

Equations of Lines and Formulas

1. Example Problems:

   • Find the equation of a line parallel to ( y = -2x + 5 ) that passes through (7,3).

   • Find the line parallel to ( 4x + 2y = 14 ) that passes through (2, 2).

   • Determine the equation of a line perpendicular to ( y = -\frac{1}{2}x - 5 ) through (6, -4).

   • Solve equations that represent relationships between angles in geometric configurations.

Angles and Triangles

• Be able to calculate measures of angles based on given information (e.g., complementary, supplementary).

• Understand properties of isosceles triangles and the significance of congruent sides.

• Apply properties of parallel lines cut by transversals to find missing angle measures.

• Work with centroid, medians, and the relationships between the parts in triangles.

Tips for Exam Preparation

• Review and memorize all formulas, facts, and definitions provided in the chart at the beginning of the review sheet.

• Practice problems geared towards calculating slopes, distances, and angles.

• Familiarize yourself with proofs regarding triangle properties, including isosceles and right triangles.

• Work on sample problems involving points of concurrency and transformations in geometry.