Download Geo 1 and 2 review answers

Definition & Theorems
Chapter 1
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acute angle – An angle whose measure is greater than zero and less than 90°.
angle – A figure formed by two rays with a common endpoint.
angle measure – The amount of degrees in an angle.
bisect – To divide a segment or angle into two congruent parts.
bisector – The line that divides the segment or angle into two congruent parts.
collinear – Lying on the same line.
congruent – The same size and shape.
congruent angles – Angles that have the same measure.
congruent segments – Segments that have the same length.
counterexample – One case that disproves a conclusion.
definition – Set forth the meaning of.
line - An infinite number of points extending in opposite directions.
line segment – Part of a line with two endpoints.
measure – The amount in something.
midpoint – A point that divides a segment into two congruent parts.
minute – A division of degrees. Sixty minutes are in one degree.
noncollinear – Not lying on the same line.
obtuse angle – An angle whose measure is greater than 90° and less than 180°.
point – The representation of a location that has no size or shape.
postulate – An unproved assumption.
ray – Part of a line with one endpoint.
right angle - An angle whose measure is 90°.
second – A division of a minute. Sixty seconds are in one minute.
segment – See line segment.
straight angle – An angle whose measure is 180°.
theorem – A mathematical statement that can be proved.
triangle – A three sided polygon.
trisect – To divide a segment or angle into three congruent parts.
trisector – The line that divides a segment or angle into three congruent parts.
trisection points – The two points at which the segment is trisected.
vertex – The common endpoint of two rays that form an angle.
The common endpoint of two sides of a polygon.
31. zero angle – An angle whose measure is 0°.
Theorems
1. If two angles are right angles, then they are congruent.
2. If two angles are straight angles, they are congruent.
Chapter 2:
Vocabulary
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complementary angles – Two angles whose sum is 90°.
oblique lines – Two intersecting lines that are not perpendicular.
opposite rays – Two collinear rays that have a common endpoint and extend in opposite directions.
perpendicular lines – Lines that intersect to form a 90° angle.
supplementary angles – Two angles whose sum is 180°.
vertical angles – A pair of angles such that the rays forming the sides of one and the rays forming the sides of the
other are opposite rays.
Theorems
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If angles are supplementary to the same angle, then they are congruent.
If angles are supplementary to congruent angles, then they are congruent.
If angles are complementary to the same angle, then they are congruent.
If angles are complementary to congruent angles, then they are congruent.
Addition Property
a) If a segment is added to two congruent segments, the sums are congruent.
b) If congruent segments are added to congruent segments, the sums are congruent.
c) If an angle is added to two congruent angles, the sums are congruent.
d) If congruent angles are added to congruent angle, the sums are congruent.
Subtraction Property
a) If a segment is subtracted to two congruent segments, the differences are congruent.
b) If congruent segments are subtracted to congruent segments, the differences are congruent.
c) If an angle is subtracted to two congruent angles, the differences are congruent.
d) If congruent angles are subtracted to congruent angle, the differences are congruent.
Multiplication Property
a) If segments are congruent, their like multiples are congruent.
b) If angles are congruent, their like multiples are congruent.
Division Property
a) If segments are congruent, their like divisions are congruent.
b) If angles are congruent, their like divisions are congruent.
Transitive Property
Symmetric Property
Reflexive Property
Vertical angles are congruent
Procedure for Drawing Conclusions (Proofs)
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Memorize theorems, definitions, and postulates.
Look for key words and symbols in the given information.
Think of all the theorems, definitions, and postulates that involve those keys
Decide which theorems, definitions, or postulates allows you to draw a conclusion.
5. Draw a conclusion, and give a reason to justify the conclusion.