Download D6 - Vocab and Ref Sheet

CP1 Math 2 Name___________________ Unit 1: Deductive Geometry Geometry Vocabulary & Proof-­‐Writing Reference Sheet •
Angle Bisector -­‐ A ray that divides an angle into two congruent parts •
Median -­‐ A segment from a vertex of a triangle to the midpoint of the opposite side •
Altitude -­‐ A perpendicular segment from a vertex of a triangle to the opposite side •
Equilateral Triangle -­‐ A triangle with three congruent sides •
Complementary Angles -­‐ Two angles whose sum is 90 degrees •
Midpoint -­‐ A point that divides a segment into two congruent parts •
Right Angle -­‐ An angle whose measure is 90 degrees •
Bisect -­‐ To divide a segment or an angle into two congruent parts •
Isosceles Triangle -­‐ A triangle in which at least two sides are congruent •
Concurrent Lines -­‐ Three or more lines that meet or intersect at one point •
Ray -­‐ A straight set of points that begins at an endpoint and extends infinitely in one direction •
Supplementary Angles -­‐ Two angles whose sum is 180 degrees •
Scalene Triangle -­‐ A triangle in which no two sides are congruent •
Parallel Lines -­‐ Coplanar lines that do not intersect •
Collinear Points -­‐ Three or more points that are on the same line •
Straight Angle -­‐ An angle whose measure is 180 degrees •
Trisect -­‐ To divide a segment or angle into three congruent parts •
Transversal -­‐ A line that intersects two coplanar lines in two distinct points •
Linear Pair -­‐ A pair of adjacent angles that form a straight line •
Right Triangle -­‐ A triangle in which one of the angles measures 90 degrees •
Quadrilateral -­‐ A four-­‐sided polygon •
Vertex -­‐ The common endpoint of two sides of a polygon •
Acute Triangle -­‐ A triangle in which all three angles are between 0 and 90 degrees •
Diagonal -­‐ A segment that joins two nonconsecutive vertices of a polygon •
Perpendicular Bisector -­‐ A line that bisects and is perpendicular to a segment •
Invariant -­‐ A quantity or expression that is constant throughout a certain range of conditions. There are numerical invariants (algebraic) and spatial invariants (geometric). Invariants can be numbers, relationships between numbers, shapes, and relationships between shapes. The following properties will be helpful to know as we begin writing proofs: Properties of Equality • Addition Property If a = b and c = d , then a + c = b + d •
Subtraction Property If a = b and c = d , then a − c = b − d •
Multiplication Property If a = b, then ca = cb •
Division Property If a = b and c ≠ 0, then
•
Substitution Property If a = b then either a or b may be substituted for the other in any equation (or inequality) •
Reflexive Property a = a •
Symmetric Property If a = b then b = a •
Transitive Property •
Distributive Property € a b
= c c
If a = d and c = d, then a = c a (b + c) = ab + ac €
Many of the properties of equality can be extended into congruence in Geometry. Here are some examples: Properties of Congruence •
Addition Property If AB ≅ WX and CD ≅ YZ, then AB + CD ≅ WX + YZ •
Reflexive Property DE ≅ DE ∠D ≅ ∠D •
Substitution Property € If ∠1 ≅ ∠2 then either ∠1 or ∠2 may substituted for the other in any equation, congruency or statement •
Transitive Property €
€
€
DE ≅ FG and FG ≅ JK then DE ≅ JK (The transitive property says that if two things are equal to the same thing, then they must be equal to each other). Other Helpful Properties •
Angle Addition An angle is the sum of its parts. Example: 𝑚∠𝐴𝑂𝐵 = 𝑚∠𝐴𝑂𝐶 + 𝑚∠𝐶𝑂𝐵 •
Segment Addition Example: 𝐴𝐶 = 𝐴𝐵 + 𝐵𝐶 A segment is the sum of its parts.