Chapter 3 Flashcards
Parallel lines
two lines that lie in the same plane and do not intersect
denoted by a ll b, triangles ► are used to indicate that the lines are parallel
Perpendicular lines
two lines that intersect to form a right angle. denoted by
a ┴ b
skew lines
two lines that do not lie in the same plane, skew lines never intersect
Parallel planes
two planes that do not intersect
line perpendicular to a plane
a line that intersects a plane in a point and that is perpendicular to every line in the plane that intersects it.
Theroms 3.1 and 3.2
Perpendicular lines
Theorem 3.1: All right angles are congruent
Theorem 3.2: If two lines are perpendicular , then they intersect to form four right angles
Theorems 3.3 and 3.4
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Theorem 3.3: If two lines intersect to form adjacent congruent angles, then the lines are perpendicular
Theorem 3.4: If two sides of adjacent acute angles are perpendicular, then the angles are complementary
Transversal
a line that intersects two or more coplanar lines at different points
corresponding angles
two angles that occupy corresponding positions
alternate interior angles
two angles that lie between the two lines on the opposite sides of the transversal
alternate exterior angles
two angles that lie outside the two lines on the opposite side of the transversal
same-side interior angles
two angles that lie between the two lines on the same side of the transversal
Postulate 8 “Corresponding angle postulate”
If two parallel lines are cut by a transversal, then correspond angles are congruent
Theorem 3.5 “Alternate interior angles theorem”
If two parallel lines are cut by a transversal, then alternate interior angles are congruent
Theorem 3.6 “ Alternate Exterior angles theorem”
If two parallel lines ate cut by a transversal the alternate exterior angles are congruent
Theorem 3.7 “Same side interior angles theorem”
If two parallel lines are cut by a transversal, then same side interior angles are supplementary.
converse
formed by switching the hypothesis and the conclusion of an if-then statement
Postulate 9 “Corresponding Angles converse”
If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel
Theorems 3.8 and 3.9 “Alternate Interior angles converse”
“Alternate Exterior angles converse”
If two lines are cut by a transversal so that alternate interior angles are congruent, the lines are parallel
If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel.
Theorem 3.10 “same side interior angles converse”
If two lines are cut by a transversal so that same side interior angles are supplementary, then the lines are parallel
Construction
a geometric drawing that uses a limited set of tools, usually a compass and a straightedge
Geo-Activity : constructing a perpendicular to a line
pg. 143
Steps:
place the compass at point P and draw an arc that intersects line “l” twice.
Open your compass wider. Draw an arc with center A, Using the same radius, draw an arc with center B
Use a straightedge to draw PQ. PQ ┴ “l”
Postulates 10 and 11
“Parallel Postulate”
“Perpendicular Postulate”
if there is a line and a point not on the line, then there is exactly one line trough point parallel to the given line.
If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line.
Theorems 3.11 and 3.12
parallel and perpendicular
If two lines are parallel to the same line, then they are parallel to each other.
In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.
ways to show that two lines are parallel on pg. 146
look at the pictures
Translation
a slide of a figure
Image
the figure after the translation
Transformation
an operation that maps, or moves, a figure onto an image.
labeling points on the image, write the prime symbol ‘ next to the letter used in the original figure
