Study for Test 2 – Chapters 4,5 – Geometry
MATH 0470 – David Hubbard
Note: First problem is a construction – either “perpendicular bisector”, “angle bisector”, or “copy angle”.
- Quadrilaterals
- Parallelogram properties
- Opposite sides are congruent
- Opposite sides are parallel
- Consecutive angles are supplementary
- Diagonals bisect each other
- Use properties of a parallelogram to solve problems
- The parallelogram and kite
- A kite is a quadrilateral with adjacent sides congruent. One pair of opposite angles is congruent.
- For a triangle ABC with median MN, MN = ½(AB) if AB is the base and also MN is parallel to AB.
- Know how to prove a quadrilateral is a parallelogram
- Rectangle, square, and rhombus
- Rectangle – all 4 angles are right angles and diagonals are Rhombus – all 4 sides are congruent and diagonals are perpendicular
- Find the length of the diagonal of a rectangle
- Square – properties of both a rectangle and a rhombus
- Trapezoid
- Isosceles trapezoid – sides are congruent, base angles are congruent, and diagonals are congruent
- Median of a trapezoid – if MN is the median of trapezoid ABCD then MN = ½(AB +DC) and MN is parallel to both bases
- If 3 parallel lines intercept congruent segments on a transversal, any other transversal will also intercept congruent segments.
- Similar Triangles
- Ratios, rates and proportions – be able to use properties to solve proportions.
- Similar Polygons
- Be able to use proportionality relationships in geometry problems
- Proving Triangles Similar
- Be able to prove triangles are similar using AA, SAS~, SSS~.
- Know how to use CSSTP in a proof.
- The Pythagorean theorem
- Be able to determine whether a triangle is right, acute, or obtuse
- Special right triangles
- 45-45-90 triangle: Given one length be able to find the other 2
- 30-60-90 triangle: Given one length be able to find the other 2
- Segments divided proportionally
- Line parallel to one side of triangle
- 3 or more parallel lines
- Angle bisector theorem