ACE Geometry PACE 1109 Handbook

An angle measuring less than 90 degrees

A triangle which has three acute angles

Two angles that have both a vertex and a side in common but do not have any interior points in common

A figure formed by two rays having a common endpoint

Consists of two points on a circle and all points between them

Angles opposite the legs of an isosceles triangle

B is between A and C if (1) A, B and C are collinear points, and (2) AB + BC = AC

Ray OB is between ray OA and ray OC if m∠AOB and m∠BOC = m∠AOC

Means to separate into two congruent points

A line, ray or line segment that intersects the line segment at its midpoint, dividing the line segment into two congruent parts

A ray that originates at the vertex of the angle and divides it into two congruent parts

A fixed point equidistant from all points on a circle

All points in a plane equidistant from a fixed point

Points which lie on the same line

An instrument used to draw circles or arcs

Two angles whose measures have a sum of 90 degrees

Having the same length or measure

Angels that have the same measure

Segments with the same length

A geometric drawing done with only a straightedge and a compass

Congruent angles of two triangles having a one-to-one relationship with each other

Congruent sides of two triangles having a one-to-one correspondence with each other

The words for which specific meanings can be given

Is 1/360 of a circle and is the unit used to measure the size of the angle

A line segment that passes through the center of a circle with endpoints that lie on the circle

An acute triangle having three congruent sides

A triangle having three congruent sides

Consists of all the area lying outside the sides of an angle

Consists of all the area lying between the sides of the angle

A triangle with only two congruent sides

The two congruent sides of an isosceles triangle

Consists of continuous point but lacks width or height, its only dimension is length

Consists of two endpoints and all points between those two endpoints and has a definite length

Divides the segment into two congruent parts

An angle with a measure greater than 90 degrees and less than 180 degrees

Has one obtuse angle

Every element in one group or figure is matched with one, and only one, element in another group or figure

Lines that lie in the same plane but do not intersect

Lines that intersect and form right angles and they form congruent, adjacent angles

A flat surface

Deals with figures that lie in a flat surface called a plane; figures that have only the dimensions of length and width

Is the basic building block of all geometric figures

Statements that are self-evident, or seem to be true, but cannot be proved

An instrument used to measure the size of an angle

A line segment from the center of a circle to any point on the circle

Consists of an endpoint and all points along the extension in the direction the ray is drawn

An angle measuring 90 degrees

A triangle with one right angle

A triangle with none congruent sides

An angle measuring 180 degrees

Unmarked ruler used to draw lines through a given point or to draw lines through two given points

Two angles whose measures have a sum of 180 degrees

A figure formed by line segments connecting three points that are nog in the same line

Means they have no precise explanation or formal definition

The common endpoint of the two rays that form an angle

The angle formed by the legs of an isosceles triangle

Two pairs of nonadjacent angles formed by two intersecting lines

The endpoints of the sides of a triangle

If equal quantities are added to equal quantities, the sums are equal

If equal quantities are subtracted from equal quantities

If equal quantities are multiplied by equal quantities, the products are equal

If equal quantities are divided by equal quantities, the quotients are equal

The whole is equal to the sum of its parts and is greater than any part

A quantity is equal (congruent) to itself

If a first quantity is equal (congruent) to a second quantity and the second quantity is equal (congruent) to a third quantity, then the first and third quantities are equal (congruent)

A quantity may be substituted for its equal (congruent) quantity

Only one straight line can be drawn through two points; two points determine a straight line

A straight line is the shortest line connecting two points in a plane

A line segment can be bisected at only one point

Two lines in the same plane either intersect or are parallel. If two lines intersect, four angles are formed at the same point of intersection

An angle has only one bisector

All straight angles are congruent

All right angles are congruent

In a plane, only one line can be drawn through a point perpendicular to a line

If one line meets another line, the adjacent angles formed are always supplementary

Angles that are complements of the same angle, or congruent angles, are congruent

Angles that are supplements of the same angle, or congruent angles, are congruent

Vertical angles are congruent

The sum of the measures of the angles around a common vertex on one side of a line is 180 degrees

If three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent (SSS postulate)

If two sides and the included angles of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent (SAS postulate)

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent (ASA postulate)