Ch. 12.4 An Introduction to a Formal Approach to Geometry.

Question 1

What does geometry call an infinite large flat surface?

Answer 1

What is a plane?

Question 2

What are the locations on a plane called?

Answer 2

What are points?

Question 3

What is considered to be straight and extend infinietely in opposite directions?

Answer 3

What is a line?

Question 4

What are points that lie on the same line?

Answer 4

What are collinear points?

Question 5

What are two lines in the plane that do not intersect or are the same called?

Answer 5

What are parallel lines?

Question 6

What are three or more lines that contain the same point called?

Answer 6

What are concurrent lines?

Question 7

The ________ between two points A and B is the nonnegative difference of the real numbers a and b to which A and B __________.

Answer 7

The distance between two points A and B is the ___________ difference of the real numbers a and b to which A and B correspond.

Question 8

The distance from A and B is written __ or BA.

Answer 8

The distance from A and B is written AB or __.

Question 9

The numbers which are lower case letters a and b are called the ________ of a line.

Answer 9

The ________ which are lower case letters a and b are called the coordinates of a line.

Question 10

This symbol, ͍ , a line with two arrows above a coordinate pair pointing opposite ways means it is a _____.

Answer 10

What symbol means a pair of coordinates is a line?

Question 11

This symbol, __ , a plain line above a coordinate means it is a line ______.

Answer 11

What symbol above a pair of coordinates means it is a ____ segment?

Question 12

This symbol, ͢ a line with an arrow pointing right above a coordinate pair means its a ____.

Answer 12

This symbol, ͢ a line with one arrow pointing ____ above a coordinate pair means its a Ray.

Question 13

What is the union of two line segments with a common endpoint or the union of two rays with a common endpoint called?

Answer 13

What is an angle?

Question 14

What is the common endpoint of an angle called?

Answer 14

What is a vertex?

Question 15

What are the line segments that make up an angle called?

Answer 15

What are sides?

Question 16

The symbol ∠ABC is used to denote _____ ABC.

Answer 16

Which symbol is used to denote angle ABC?

Question 17

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?

Answer 17

What is a convex polygon?

Question 18

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?

Answer 18

What is a Concave polygon?

Question 19

A portion of a plane that is not the angle or the interior is called the _______.

Answer 19

What is the exterior of the angle?

Question 20

The convex region of a plane is called the _______ region.

Answer 20

The _____ region of a plane is called the interior region.

Question 21

Two angles that share a vertex, have a side in common, but whose interiors do not intersect are called ________ angles.

Answer 21

What are Adjacent Angles?

Question 22

What is the semicircle device used in geometry to measure angles called?

Answer 22

What is a protractor?

Question 23

The measurement of angle BAC is denotes by the following expression, m(∠BAC).

Answer 23

The expression m(∠BAC) is read _________.

Question 24

An angle measuring less than 90° is called a(n) ______ angle.

Answer 24

What is an acute angle?

Question 25

An angle measuring 90° is called a(n) _______ angle.

Answer 25

What is a right angle?

Question 26

An angle measuring more than 90° but less than 180° is called a(n) ________ angle.

Answer 26

What is an obtuse angle?

Question 27

An angle measuring 180° is called a _____ angle.

Answer 27

What is a straight angle?

Question 28

An angle whose measures are greater than 180° is called a(n) _______ angle.

Answer 28

What is a reflex angle?

Question 29

Any two angles that are not adjacent and have the same measure are called _____ angles.

Answer 29

What are congruent vertical angles?

Question 30

Angles having the same measure are called _____ angles.

Answer 30

What are congruent angles?

Question 31

Line segments having the same length are called _________ segments.

Answer 31

What are congruent segments?

Question 32

The symbol of an equal sign with just a tilde above (⩭) means angles or lines are ________.

Answer 32

Which symbol means that angles or lines are congruent?

Question 33

The sum of two angles whose measures equals 180° are called _________angles.

Answer 33

What are supplementary angles?

Question 34

If two lines intersect to form a right angle the lines are called _________ lines.

Answer 34

What are perpendicular lines?

Question 35

The symbol with a horizontal line and a vertical line meeting in the middle (⟂) means line a is ________ to line b.

Answer 35

Which symbol means line a is perpendicular to line b?

Question 36

The sum of two angles whose measures equals 90° are called ________ angles.

Answer 36

What are complimentary angles?

Question 37

If two lines, L and M, are intersected by a third line, T, we call line T a ___________.

Answer 37

What is a transversal?

Question 38

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.

Answer 38

What is a corresponding angle?

Question 39

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.

Answer 39

What is an alternate interior angle?

Question 40

The sum of the measures of the three vertex angles in a triangle is ______°.

Answer 40

For which shape do the vertex angles sum to 180°?

Question 41

Due to the angle sum in a triangle theory, a triangle can have at most, one _______ angle or at most one ______ angle.

Answer 41

Due to the _____-____ in a triangle theory, a triangle can have at most, one right angle or at most one obtuse angle.

Question 42

A triangle that has an angle of 90° is called a(n) ________ triangle.

Answer 42

What is a right triangle?

Question 43

A triangle that has an angle measuring more than 90°, but less than 180° is called a(n) _________ triangle.

Answer 43

What is an obtuse triangle?

Question 44

A triangle in which all the angles measure less than 90° is called a(n) ________ triangle.

Answer 44

What is an acute triangle?

Question 45

What do we call two points on a line, and all the points that lie between them?

Answer 45

What is a line segment?

Question 46

What do we call two distinct lines in the same plane that do not intersect?

Answer 46

What are parallel lines?

Question 47

What do we call the union of two segments or rays with a common endpoint?

Answer 47

What is an angle?

Question 48

What to we call an angle with a measure less than 90 degrees?

Answer 48

What is an acute angle?

Question 49

What do we call an angle that measures 90 degrees?

Answer 49

What is a right angle?

Question 50

What do we call an angle with a measure greater than 90 and less than 180?

Answer 50

What is an obtuse angle?

Question 51

What do we call an angle that measures 180 degrees?

Answer 51

What is a straight angle?

Question 52

What do we call an angle that measures more than 180 degrees?

Answer 52

What is a reflex angle?

Question 53

What do we call two angles that share a vertex and a side but no interior points?

Answer 53

What are adjacent angles?

Question 54

What do we call two nonadjacent angles formed by two intersecting lines?

Answer 54

What are vertical angles?

Question 55

What do we call two angles whose measures add to 180 degrees?

Answer 55

What are supplementary angles?

Question 56

What do we call two angles whose measures add to 90 degrees?

Answer 56

What are complimentary angles?

Question 57

What do we call two lines that intersect to form a right angle?

Answer 57

What are Perpendicular lines?

Question 58

What is a triangle with one right angle?

Answer 58

What is a right triangle?

Question 59

What is a triangle with three acute angles?

Answer 59

What is an acute triangle?

Question 60

What is a triangle with one obtuse angle?

Answer 60

What is an obtuse triangle?

Question 61

When two _____ of a triangle are congruent, the ______ opposite those _____ are congruent.

Answer 61

When two sides of a triangle are _________, the angles opposite those sides are _________.

Question 62

Since all three sides of an equilateral triangle are congruent, all three angles are congruent, making them each ______ degrees.

Answer 62

Since all three sides of an _______ triangle are congruent, all three angles are congruent, making them each 60 degrees .

Question 63

The two types of equilateral triangles that are not possible are the ________ triangle and the ________ triangle?

Answer 63

The obtuse and right triangles are two of the triangles that cannot be _____________ triangles.

Question 64

The two parallel sides of a trapezoid are called _______.

Answer 64

Which sides of a trapezoid are called bases.

Question 65

Two angles whose common side is a base of trapezoid are called _______ angles.

Answer 65

What are the base angles of a trapezoid?

Question 66

There are _____ pairs of base angles in each trapezoid, one for each base.

Answer 66

There are two pairs of _______ angles in each trapezoid, one fore each ______.

Question 67

A pair of angles in a quadrilateral that has no sides in common are called _______ angles.

Answer 67

What are opposite angles?

Question 68

A quadrilateral has _____ pairs of opposite angles.

Answer 68

A quadrilateral has two pairs of ________ angles.

Question 69

A kite has one pair of ________ angles that are congruent.

Answer 69

A kite has one pair of opposite angles that are ____________.

Question 70

A parallelogram's opposite angles are ________.

Answer 70

A parallelogram's ________ angles are congruent.

Question 71

Since a rhombus is a special kind of ____________, it also has _____ pairs of congruent opposite angles.

Answer 71

Since a rhombus is a special kind of parallelogram, it also has two pairs of congruent ________ angles.

Question 72

In a rectangle and square all ______ are 90 degrees, which means they are congruent.

Answer 72

In a rectangle and square all angles are 90 degrees which means they are ____________.

Question 73

The base angles of any isosceles trapezoid are __________.

Answer 73

The ______ angles of any isosceles trapezoid are congruent.

Question 74

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.

Answer 74

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.

Question 75

Which quadrilaterals have opposite sides congruent? one has 1 pair of congruent opposite sides; the other four have two pairs.

Answer 75

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.

Question 76

In which two quadrilaterals are all angles 90 degrees and considered congruent?

Answer 76

All the angles in a rectangle and square are 90 degrees and considered __________.

Question 77

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.

Answer 77

The trapezoid, isosceles trapezoid have _____ pair of opposite parallel sides; the parallelogram, rhombus, rectangle and square have ____ pairs of opposite parallel sides.

Question 78

In which two quadrilaterals are the adjacent sides always perpendicular?

Answer 78

In a rectangle and square the adjacent sides are always _____________.

Question 79

In which quadrilaterals are both diagonals congruent?

Answer 79

Diagonals are always ________ in isosceles trapezoid, rectangle and square.

Question 80

In which four quadrilaterals do diagonals intersect at the midpoint?

Answer 80

A parallelogram, rhombus, rectangle and square all have diagonals that intersect at the _________.

Question 81

In which three quadrilaterals are the diagonals perpendicular?

Answer 81

In a kite, rhombus, and square the diagonals are __________.

Question 82

In which five quadrilaterals are the opposite angles congruent? One has one pair and the other four simply have opposite angles congruent.

Answer 82

A kite (only 1 pair), parallelogram, rhombus, rectangle and square all have opposite angles that are __________.

Question 83

The _______ trapezoid is the only quadrilateral whose base angles are congruent.

Answer 83

The isosceles trapezoid is the only quadrilateral whose _________ angles are congruent.

Question 84

In which quadrilaterals are opposite angles bisected by a diagonal? One has only one pair and the other two have two pair.

Answer 84

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.