Math 3
Terms
undefined, object
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- theorem of lines associated with triangles
- the centroid of a triangle is located 2/3 of the distance from each vertex to the midpoint of the opposite side
- examples of undefined words
- point, line, plane
- theorem or deductive reasoning
- the shortest segment from a point not on a line is the perpendicular segment
- scalene triangle
- no 2 sides are congruent
- Examples of undefined terms:
- point end line
- theorems about angles in special triangles
- each angle of an equilateral measures 60 degrees
- organizing proof
- proof equals a sequence of true statements placed in a logical order
- one property that does change when reflected over a line
- the orientation of the figures is "flipped" or reversed
- theorem of angles outside the triangle
- follows immediately from antoher is called a corollary
- exterior angle inequality theorem
- the measure of exterior angles of a triangle is greater than the measure of either of its remote interor angles
- orientation of a figure
- can be clockwise or counter clockwise
- Side-Angle-Angle SAA Postulate*
- If it looks like this then it is congruent
- Deductive Reasoning
- the process of drawing conclusionns from given information by using rules of logic. In deductive reasoning, we must be able to justify any statement that we make.
- correspondence between two geometric figures
- is any way of pairing up their vertices. A congruence correspondence matches the vertices so that all pairs of corresponding parts are congruent
- equilateral triangle
- all sides are congruent
- figure is reflected over a line if,
- measures of the line segments stay the same; measures of all angles stay the same; figures have same area; figures have same perimeter
- Isosceles triangle
- at least 2 of its sides are congruent
- Inductive Reasoning
- makes conjectures based on patterns and examples
- Construction angle congruent to another*
- *
- types of proof statements include
- given inforemation; info that can be assumed by athe figure; definitions; postulates; algebraic properties;theorems that have alread been proved
- concurrent lines
- 3 + plane lines intersectanting at the same pont
- centroid
- the concurrency of the medians of any centroid
- pre-image
- original figure
- A tessellation
- a repeating pattern of figures that completely covers a plane region without gaps or overlaps
- point of concurrency
- the point of intersection
- exteriof angle theorem
- measures of an exterior angle is equal to the sume of its remote interior angles
- symmetric congruence
- *
- image
- image after the transformation
- chain rule
- links 2 conditional statements
- theorem of corresponding parts
- corresponding parts of congruent triangles are congruent
- Side-Angle-Side SAS Postulate*
- If it looks like this then it is congruent
- construct perpendicular line *
- *
- Side-Side-Side SSS Postulate*
- If it looks like this then it is congruent
- symbol for corrresponds
- to is a line with arrows on either end. The order of the letters in the statement specifies the corrresponding sides and angles
- law of detachment
- if you are given a true conditional statement and you know the hypothesis is true, then the conclusion must also be true. (detaching the conclusion from the hypothesis)
- Angle-Side-Angle ASA Postulate*
- If it looks like this then it is congruent
- congurent triangles
- two triangles are congruent if and only if all of their coresponding parts are congruent
- transitive congruence
- *
- reflexsive congruence
- *
- Examples of defined terms:
- Line segment