Name:______

Geometry Semester 1 Study Guide

Chapter 1: Basics of Geometry

  1. Compare and contrast: Lines, Line Segments, Rays
  1. Describe the Segment Addition Postulate.
  1. Given the coordinates of two points, how do you find their midpoint? How do you find the distance between them? List formulas if necessary.
  1. What is the difference between a concave and a convex polygon? Draw an example of each.
  1. What is a linear pair? If two angles form a linear pair and one is bigger than the other, what do you know about the angles?
  1. Define each type of angle relationship: complementary angles, supplementary angles, adjacent angles, vertical angles (drawing a sketch is recommended).

Chapter 2: Reasoning and Proofs

  1. Write the converse, inverse, and contrapositive of the statement: “If you build it, they will come.” (double points if you get that reference).
  1. Use the Laws of Syllogism and Detachment to make a conclusion: “If Dory sees a whale, she will speak like a whale. If Dory speaks like a whale, the whale will come over to say hi. Dory just spotted Bailey the Beluga.”
  1. What is the name of the property of equality that says that a segment is equal to itself?
  1. Describe the basic steps for writing a proof.
  1. What are vertical angles? What is special about them?

Chapter 3: Parallel and Perpendicular Lines

  1. What is a transversal? Name and sketch the four different angle pair relationships created by a transversal.
  1. When the lines cut by a transversal are parallel, which angle pairs are congruent? Which angle pairs are supplementary?
  1. How can you use angle pairs to show that two lines are parallel?
  1. How do you measure the distance from a point to a line? Draw a sketch to help your explanation.
  1. If two lines form a linear pair of congruent angles, what can you conclude about the lines?
  1. How do you write the equation of a line that is parallel to another line through a given point?
  1. How is writing the equation of a perpendicular line different from writing the equation of a parallel line?

Chapter 4: Transformations

  1. Which type of transformation moves a figure? What is the coordinate rule for this transformation if moved by the vector ?
  1. Which type of transformation might be called a “flip”? What are the coordinate rules for this transformation when flipped over: the axis, the axis, the line , the line ?
  1. Which type of transformation might be called a “turn”? What are the coordinate rules for this transformation when turned: (assume clockwise—what would be the counter-clockwise rules?)?
  1. Reflecting over two parallel lines is equivalent to a ______that is ______as far as the distance between the lines.
  2. Reflecting over two intersecting lines is equivalent to a ______that is double the angle ______.
  3. Which type of transformation makes the figure change size proportionately? What is the coordinate rule for this transformation if stretched by a scale factor of k? When does the figure get bigger/smaller?
  1. Which transformations are congruence transformations? Which transformations are similarity transformations?

Chapter 5: Congruent Triangles

  1. Explain the Exterior Angle Theorem (for triangles) in your own words. Draw a sketch to support your explanation.
  1. If , name all pairs of congruent angles and all pairs of congruent sides.
  2. Explain the Third Angles Theorem (for triangles) in your own words. Draw a sketch to support your explanation.
  1. What are the five different congruence shortcuts we can use to prove that triangles are congruent?
  2. If an isosceles triangle has an angle that measures , find two different possibilities for the measures of the other two angles.
  1. What do the angles of an equilateral triangle equal? How can you explain why this will ALWAYS be true?
  1. If you have and , what should you do to prove that any two corresponding parts are congruent?

Chapter 6: Relationships Within Triangles

  1. What is true about any point on the perpendicular bisector of a segment? On the bisector of an angle?
  1. Name the points of concurrency of each type of segment: altitude, angle bisector, median, perpendicular bisector.
  1. Draw a diagram to represent the different lengths created by a vertex, centroid, and ______of the opposite side:
  1. What is a midsegment of a triangle? What two special properties does a midsegment have with one side of the triangle?
  1. Complete the statement: the largest side of any triangle is ______.
  2. If a triangle has side lengths a and b, write an inequality to represent the possible lengths of the third side, x.
  1. Given with , and given , which of the six angles it the biggest? How do you know?