Ch. 12.4 An Introduction to a Formal Approach to Geometry. Flashcards
What does geometry call an infinite large flat surface?
What is a plane?
What are the locations on a plane called?
What are points?
What is considered to be straight and extend infinietely in opposite directions?
What is a line?
What are points that lie on the same line?
What are collinear points?
What are two lines in the plane that do not intersect or are the same called?
What are parallel lines?
What are three or more lines that contain the same point called?
What are concurrent lines?
The ________ between two points A and B is the nonnegative difference of the real numbers a and b to which A and B __________.
The distance between two points A and B is the ___________ difference of the real numbers a and b to which A and B correspond.
The distance from A and B is written __ or BA.
The distance from A and B is written AB or __.
The numbers which are lower case letters a and b are called the ________ of a line.
The ________ which are lower case letters a and b are called the coordinates of a line.
This symbol, ͍ , a line with two arrows above a coordinate pair pointing opposite ways means it is a _____.
What symbol means a pair of coordinates is a line?
This symbol, __ , a plain line above a coordinate means it is a line ______.
What symbol above a pair of coordinates means it is a ____ segment?
This symbol, ͢ a line with an arrow pointing right above a coordinate pair means its a ____.
This symbol, ͢ a line with one arrow pointing ____ above a coordinate pair means its a Ray.
What is the union of two line segments with a common endpoint or the union of two rays with a common endpoint called?
What is an angle?
What is the common endpoint of an angle called?
What is a vertex?
What are the line segments that make up an angle called?
What are sides?
The symbol ∠ABC is used to denote _____ ABC.
Which symbol is used to denote angle ABC?
What type of shape can one pick any two points in the interior of a polygon, connect the and the line segment is always inside?
What is a convex polygon?
What type of shape can one pick any two points in the interior of the polygon, which when connected does not lie entirely inside the polygon?
What is a Concave polygon?
A portion of a plane that is not the angle or the interior is called the _______.
What is the exterior of the angle?
The convex region of a plane is called the _______ region.
The _____ region of a plane is called the interior region.
Two angles that share a vertex, have a side in common, but whose interiors do not intersect are called ________ angles.
What are Adjacent Angles?
What is the semicircle device used in geometry to measure angles called?
What is a protractor?
The measurement of angle BAC is denotes by the following expression, m(∠BAC).
The expression m(∠BAC) is read _________.
An angle measuring less than 90° is called a(n) ______ angle.
What is an acute angle?
An angle measuring 90° is called a(n) _______ angle.
What is a right angle?
An angle measuring more than 90° but less than 180° is called a(n) ________ angle.
What is an obtuse angle?
An angle measuring 180° is called a _____ angle.
What is a straight angle?
An angle whose measures are greater than 180° is called a(n) _______ angle.
What is a reflex angle?
Any two angles that are not adjacent and have the same measure are called _____ angles.
What are congruent vertical angles?
Angles having the same measure are called _____ angles.
What are congruent angles?
Line segments having the same length are called _________ segments.
What are congruent segments?
The symbol of an equal sign with just a tilde above (⩭) means angles or lines are ________.
Which symbol means that angles or lines are congruent?
The sum of two angles whose measures equals 180° are called _________angles.
What are supplementary angles?
If two lines intersect to form a right angle the lines are called _________ lines.
What are perpendicular lines?
The symbol with a horizontal line and a vertical line meeting in the middle (⟂) means line a is ________ to line b.
Which symbol means line a is perpendicular to line b?
The sum of two angles whose measures equals 90° are called ________ angles.
What are complimentary angles?
If two lines, L and M, are intersected by a third line, T, we call line T a ___________.
What is a transversal?
When lines L and M are intersected by a transversal and L is Parallel to M (L || M) then angle 1 and 2 are ___________ angles.
What is a corresponding angle?
When lines L and M are intersected by a transversal and L is Parallel to M (L || M) then the non adjacent angles (2 & 3) formed are ___________-___________ angles.
What is an alternate interior angle?
The sum of the measures of the three vertex angles in a triangle is ______°.
For which shape do the vertex angles sum to 180°?
Due to the angle sum in a triangle theory, a triangle can have at most, one _______ angle or at most one ______ angle.
Due to the _____-____ in a triangle theory, a triangle can have at most, one right angle or at most one obtuse angle.
A triangle that has an angle of 90° is called a(n) ________ triangle.
What is a right triangle?
A triangle that has an angle measuring more than 90°, but less than 180° is called a(n) _________ triangle.
What is an obtuse triangle?
A triangle in which all the angles measure less than 90° is called a(n) ________ triangle.
What is an acute triangle?
What do we call two points on a line, and all the points that lie between them?
What is a line segment?
What do we call two distinct lines in the same plane that do not intersect?
What are parallel lines?
What do we call the union of two segments or rays with a common endpoint?
What is an angle?
What to we call an angle with a measure less than 90 degrees?
What is an acute angle?
What do we call an angle that measures 90 degrees?
What is a right angle?
What do we call an angle with a measure greater than 90 and less than 180?
What is an obtuse angle?
What do we call an angle that measures 180 degrees?
What is a straight angle?
What do we call an angle that measures more than 180 degrees?
What is a reflex angle?
What do we call two angles that share a vertex and a side but no interior points?
What are adjacent angles?
What do we call two nonadjacent angles formed by two intersecting lines?
What are vertical angles?
What do we call two angles whose measures add to 180 degrees?
What are supplementary angles?
What do we call two angles whose measures add to 90 degrees?
What are complimentary angles?
What do we call two lines that intersect to form a right angle?
What are Perpendicular lines?
What is a triangle with one right angle?
What is a right triangle?
What is a triangle with three acute angles?
What is an acute triangle?
What is a triangle with one obtuse angle?
What is an obtuse triangle?
When two _____ of a triangle are congruent, the ______ opposite those _____ are congruent.
When two sides of a triangle are _________, the angles opposite those sides are _________.
Since all three sides of an equilateral triangle are congruent, all three angles are congruent, making them each ______ degrees.
Since all three sides of an _______ triangle are congruent, all three angles are congruent, making them each 60 degrees .
The two types of equilateral triangles that are not possible are the ________ triangle and the ________ triangle?
The obtuse and right triangles are two of the triangles that cannot be _____________ triangles.
The two parallel sides of a trapezoid are called _______.
Which sides of a trapezoid are called bases.
Two angles whose common side is a base of trapezoid are called _______ angles.
What are the base angles of a trapezoid?
There are _____ pairs of base angles in each trapezoid, one for each base.
There are two pairs of _______ angles in each trapezoid, one fore each ______.
A pair of angles in a quadrilateral that has no sides in common are called _______ angles.
What are opposite angles?
A quadrilateral has _____ pairs of opposite angles.
A quadrilateral has two pairs of ________ angles.
A kite has one pair of ________ angles that are congruent.
A kite has one pair of opposite angles that are ____________.
A parallelogram’s opposite angles are ________.
A parallelogram’s ________ angles are congruent.
Since a rhombus is a special kind of ____________, it also has _____ pairs of congruent opposite angles.
Since a rhombus is a special kind of parallelogram, it also has two pairs of congruent ________ angles.
In a rectangle and square all ______ are 90 degrees, which means they are congruent.
In a rectangle and square all angles are 90 degrees which means they are ____________.
The base angles of any isosceles trapezoid are __________.
The ______ angles of any isosceles trapezoid are congruent.
Which quadrilaterals have adjacent sides that are congruent? One has one pair of adjacent sides that are congruent and the other two have all pairs congruent.
The following quadrilaterals have adjacent sides that are congruent, tell how many congruent pairs each has.
A Kite has ___ pair; a rhombus and a square have _____ pairs.
Which quadrilaterals have opposite sides congruent? one has 1 pair of congruent opposite sides; the other four have two pairs.
The following quadrilaterals have opposite sides that are congruent, tell how many congruent pairs each has. the Isosceles trapezoid has __ pair of opposite congruent sides; The other four: a parallelogram, rhombus, rectangle and square all have ___ pairs of opposite congruent sides.
In which two quadrilaterals are all angles 90 degrees and considered congruent?
All the angles in a rectangle and square are 90 degrees and considered __________.
In which six quadrilaterals are the opposite sides parallel? Two have one pair of opposite parallel sides; the other four have two pairs of opposite parallel sides.
The trapezoid, isosceles trapezoid have _____ pair of opposite parallel sides; the parallelogram, rhombus, rectangle and square have ____ pairs of opposite parallel sides.
In which two quadrilaterals are the adjacent sides always perpendicular?
In a rectangle and square the adjacent sides are always _____________.
In which quadrilaterals are both diagonals congruent?
Diagonals are always ________ in isosceles trapezoid, rectangle and square.
In which four quadrilaterals do diagonals intersect at the midpoint?
A parallelogram, rhombus, rectangle and square all have diagonals that intersect at the _________.
In which three quadrilaterals are the diagonals perpendicular?
In a kite, rhombus, and square the diagonals are __________.
In which five quadrilaterals are the opposite angles congruent? One has one pair and the other four simply have opposite angles congruent.
A kite (only 1 pair), parallelogram, rhombus, rectangle and square all have opposite angles that are __________.
The _______ trapezoid is the only quadrilateral whose base angles are congruent.
The isosceles trapezoid is the only quadrilateral whose _________ angles are congruent.
In which quadrilaterals are opposite angles bisected by a diagonal? One has only one pair and the other two have two pair.
A kite has one pair of opposite angles _________ by a diagonal and the rhombus and square have two pairs of opposite angles _________ by a diagonal.
