Mathematics for Elementary Educators
III - D127 Exam Questions With Certified
Answers
Points - AnswerThe most fundamental geometric concept. A location, or position. It has
no size or shape and is defined by its only property: its position. (*)
/.Line Segments - AnswerConsists of two endpoints and all the points between those
endpoints. The order of the points does not matter in naming the line segment. (*-*)
/.Rays - AnswerHas a single endpoint (also called its origin) and extends indefinitely in
one direction. The ray's direction is described with the help of any other point on the ray.
(-->)
/.Lines - AnswerContinue infinitely in opposite directions. The fact that lines continue
forever in opposite directions is what sets lines apart from line segments and rays. (<->)
/.Angle - AnswerYou can measure the relationship between two lines by measuring the
angle between them.
/.Degree - AnswerAngles can be measured in degrees, which are denoted by the
symbol "°".
/.Straight Angle - AnswerA straight line is also called a straight angle. The measure of
an angle that lies on a straight line is 180°.
/.Right Angle - AnswerA 90° angle is called a right angle. Please note that a right angle
is denoted by the symbol ┐between the two lines, as shown above. When you see this
symbol, you can be confident you are seeing a right angle.
/.Acute Angles - AnswerMeasure less than 90°.
/.Obtuse Angles - AnswerMeasure greater than 90°, but less than 180°.
/.Straight Angles - AnswerMeasure exactly 180°.
/.Reflex Angles - AnswerMeasure greater than 180°.
/.Supplementary Angle - AnswerTwo angles that add up to 180°, respectively.
/.Complementary Angle - AnswerTwo angles that add up to 90°, respectively.
, /.Polygon - AnswerA closed geometric figure with at least three straight sides.
/.Vertex - AnswerThe point where two sides meet is called a vertex. (The plural of vertex
is vertices.)
/.Regular Polygon - AnswerHas equal sides and equal angles.
/.Irregular Polygon - AnswerHas sides that are not all the same length and interior
angles that are not all the same measure.
/.Quadrilateral - AnswerA polygon with four sides and four vertices. Other polygons
have different numbers of sides: a pentagon has five sides; a hexagon has six sides.
/.Interior Angle - AnswerAn angle inside a polygon that is formed by two adjacent sides.
The sum of the interior angles of all polygons (both regular and irregular) can be found
with the formula. (180°(n−2))
/.Triangle - AnswerThe building blocks for other shapes. Triangles are polygons with
three sides and three angles, and the sum of the interior angles of a triangle* is 180°.
There are three basic types of triangles.
/.Equilateral Triangles - AnswerHave three equal angles (each measuring 60°). The
three sides of any given equilateral triangle have the same length.
/.Isosceles Triangles - AnswerHave only 2 equal angles. In an isosceles triangle, only
two sides will have the same length. Notice that the same length sides are opposite the
angles that have the same measure.
/.Scalene Triangles - AnswerHave three angles of different sizes. In a scalene triangle,
each side will have a different length.
/.The Triangle Inequality Theorem - AnswerStates that for every triangle, the sum of any
two sides is always greater than the third side.
/.Diagonal - AnswerA line segment whose endpoints are nonconsecutive vertices of the
figure. A diagonal is not a side of the quadrilateral. The diagonals of different types of
quadrilaterals have certain properties.
/.Parallelogram - AnswerAny four-sided shape that has opposite, parallel sides that are
equal in length, and, therefore, opposite angles that are equal in size. Some
quadrilaterals can be correctly identified only as parallelograms. Others, like squares,
rectangles, and rhombuses, are all also parallelograms, but they have special
properties. Like all parallelograms, squares, rectangles, and rhombuses have opposite
parallel and equal sides and two sets of equal opposite angles, but they have the
III - D127 Exam Questions With Certified
Answers
Points - AnswerThe most fundamental geometric concept. A location, or position. It has
no size or shape and is defined by its only property: its position. (*)
/.Line Segments - AnswerConsists of two endpoints and all the points between those
endpoints. The order of the points does not matter in naming the line segment. (*-*)
/.Rays - AnswerHas a single endpoint (also called its origin) and extends indefinitely in
one direction. The ray's direction is described with the help of any other point on the ray.
(-->)
/.Lines - AnswerContinue infinitely in opposite directions. The fact that lines continue
forever in opposite directions is what sets lines apart from line segments and rays. (<->)
/.Angle - AnswerYou can measure the relationship between two lines by measuring the
angle between them.
/.Degree - AnswerAngles can be measured in degrees, which are denoted by the
symbol "°".
/.Straight Angle - AnswerA straight line is also called a straight angle. The measure of
an angle that lies on a straight line is 180°.
/.Right Angle - AnswerA 90° angle is called a right angle. Please note that a right angle
is denoted by the symbol ┐between the two lines, as shown above. When you see this
symbol, you can be confident you are seeing a right angle.
/.Acute Angles - AnswerMeasure less than 90°.
/.Obtuse Angles - AnswerMeasure greater than 90°, but less than 180°.
/.Straight Angles - AnswerMeasure exactly 180°.
/.Reflex Angles - AnswerMeasure greater than 180°.
/.Supplementary Angle - AnswerTwo angles that add up to 180°, respectively.
/.Complementary Angle - AnswerTwo angles that add up to 90°, respectively.
, /.Polygon - AnswerA closed geometric figure with at least three straight sides.
/.Vertex - AnswerThe point where two sides meet is called a vertex. (The plural of vertex
is vertices.)
/.Regular Polygon - AnswerHas equal sides and equal angles.
/.Irregular Polygon - AnswerHas sides that are not all the same length and interior
angles that are not all the same measure.
/.Quadrilateral - AnswerA polygon with four sides and four vertices. Other polygons
have different numbers of sides: a pentagon has five sides; a hexagon has six sides.
/.Interior Angle - AnswerAn angle inside a polygon that is formed by two adjacent sides.
The sum of the interior angles of all polygons (both regular and irregular) can be found
with the formula. (180°(n−2))
/.Triangle - AnswerThe building blocks for other shapes. Triangles are polygons with
three sides and three angles, and the sum of the interior angles of a triangle* is 180°.
There are three basic types of triangles.
/.Equilateral Triangles - AnswerHave three equal angles (each measuring 60°). The
three sides of any given equilateral triangle have the same length.
/.Isosceles Triangles - AnswerHave only 2 equal angles. In an isosceles triangle, only
two sides will have the same length. Notice that the same length sides are opposite the
angles that have the same measure.
/.Scalene Triangles - AnswerHave three angles of different sizes. In a scalene triangle,
each side will have a different length.
/.The Triangle Inequality Theorem - AnswerStates that for every triangle, the sum of any
two sides is always greater than the third side.
/.Diagonal - AnswerA line segment whose endpoints are nonconsecutive vertices of the
figure. A diagonal is not a side of the quadrilateral. The diagonals of different types of
quadrilaterals have certain properties.
/.Parallelogram - AnswerAny four-sided shape that has opposite, parallel sides that are
equal in length, and, therefore, opposite angles that are equal in size. Some
quadrilaterals can be correctly identified only as parallelograms. Others, like squares,
rectangles, and rhombuses, are all also parallelograms, but they have special
properties. Like all parallelograms, squares, rectangles, and rhombuses have opposite
parallel and equal sides and two sets of equal opposite angles, but they have the
