1.7: Chapter 1 Review
Symbol Toolbox
\begin{align*}\overleftrightarrow{AB}, \ \overrightarrow{AB}, \ \overline{AB}\end{align*}
\begin{align*}\angle ABC\end{align*}
\begin{align*}m \overline{AB} \ \text{or} \ AB\end{align*}
\begin{align*}m \angle ABC\end{align*}
\begin{align*}\bot\end{align*}
\begin{align*}=\end{align*}
\begin{align*}\cong\end{align*}
Keywords
 Geometry
 Geometry is founded upon some very important basic concepts. These include points, angles, lines, and line segments.
 Point
 An exact location in space.
 Line
 Infinitely many points that extend forever in both directions.
 Plane
 Infinitely many intersecting lines that extend forever in all directions.
 Space
 The set of all points expanding in three dimensions.
 Collinear
 Points that lie on the same line.
 Coplanar
 Points and/or lines within the same plane.
 Endpoint
 A point at the end of a line.
 Line Segment
 Part of a line with two endpoints. Or a line that stops at both ends.
 Ray
 Part of a line with one endpoint and extends forever in the other direction.
 Intersection
 A point or set of points where lines, planes, segments or rays cross each other
 Postulates
 Basic rules of geometry.
 Theorem
 A statement that can be proven true using postulates, definitions, and other theorems that have already proven.
 Distance
 How far apart two geometric objects are.
 Measure
 Angles are classified by their measure.
 Ruler Postulate
 The distance between two points will be the absolute value of the difference between the numbers shown on the ruler.
 Segment Addition Postulate
 The measure of any line segment can be found by adding the measures of the smaller segments that make it up

If \begin{align*}A\end{align*}
A , \begin{align*}B\end{align*}B , and \begin{align*}C\end{align*}C are collinear and \begin{align*}B\end{align*}B is between \begin{align*}A\end{align*}A and \begin{align*}C\end{align*}C , then \begin{align*}AB + BC = AC\end{align*}AB+BC=AC .
 Angle
 When two rays have the same endpoint.
 Vertex
 The common endpoint of the two rays that form an angle.
 Sides
 The two rays that form an angle.
 Protractor Postulate

For every angle there is a number between \begin{align*}0^\circ\end{align*}
0∘ and \begin{align*}180^\circ\end{align*}180∘ that is the measure of the angle in degrees. The angle's measure is then the absolute value of the difference of the numbers shown on the protractor where the sides of the angle intersect the protractor.
 Straight Angle

When an angle measures \begin{align*}180^\circ\end{align*}
180∘ . The angle measure of a straight line.
 Right Angle

When an angle measures \begin{align*}90^\circ\end{align*}
90∘ .
 Acute Angles

Angles that measure between \begin{align*}0^\circ\end{align*}
0∘ and \begin{align*}90^\circ\end{align*}90∘ .
 Obtuse Angles

Angles that measure between \begin{align*}90^\circ\end{align*}
90∘ and \begin{align*}180^\circ\end{align*}180∘ .
 Perpendicular
 When two lines intersect to form four right angles.
 Construction
 Anytime we use a compass and ruler to draw different geometric figures, it called a construction.
 Compass
 A tool used to draw circles and arcs.
 Angle Addition Postulate
 The measure of any angle can be found by adding the measures of the smaller angles that comprise it.

If \begin{align*}B\end{align*}
B is on the interior of \begin{align*}\angle ADC\end{align*}∠ADC , then \begin{align*}m \angle ADC = m \angle ADB + m \angle BDC\end{align*}m∠ADC=m∠ADB+m∠BDC .
 Congruent
 When two geometric figures have the same shape and size.
 Midpoint
 A point on a line segment that divides it into two congruent segments
 Midpoint Postulate
 Any line segment will have exactly one midpoint.
 Segment Bisector
 A line, segment, or ray that passes through a midpoint of another segment.
 Perpendicular Bisector
 A line, ray or segment that passes through the midpoint of another segment and intersects the segment at a right angle.
 Perpendicular Bisector Postulate
 For every line segment, there is one perpendicular bisector that passes through the midpoint.
 Angle Bisector
 A ray that divides an angle into two congruent angles, each having a measure exactly half of the original angle.
 Angle Bisector Postulate
 Every angle has exactly one angle bisector.
 Complementary

When two angles add up to \begin{align*}90^\circ\end{align*}
90∘ .
 Supplementary

When two angles add up to \begin{align*}180^\circ\end{align*}
180∘ .
 Adjacent Angles
 Two angles that have the same vertex, share a side, and do not overlap.
 Linear Pair
 Two angles that are adjacent and whose noncommon sides form a straight line.
 Linear Pair Postulate
 If two angles are a linear pair, then they are supplementary.
 Vertical Angles
 Two nonadjacent angles formed by intersecting lines.
 Vertical Angles Theorem
 If two angles are vertical angles, then they are congruent.
 Triangle
 Any closed figure made by three line segments intersecting at their endpoints.
 Right Triangle
 When a triangle has one right angle.
 Obtuse Triangle
 When a triangle has one obtuse angle.
 Acute Triangle
 When all three angles in the triangle are acute.
 Equiangular Triangle
 When all the angles in a triangle are congruent.
 Scalene Triangle
 When a triangles sides are all different lengths.
 Isosceles Triangle
 A triangle with at least two sides of equal length.
 Equilateral Triangle
 A triangle with three sides of equal length.
 Polygon
 Any closed planar figure that is made entirely of line segments that intersect at their endpoints.
 Diagonals
 Line segments that connects the vertices of a convex polygon that are not sides.
Review
Match the definition or description with the correct word.
 When three points lie on the same line. — A. Measure
 All vertical angles are ________. — B. Congruent
 Linear pairs add up to _______. — C. Angle Bisector
 The \begin{align*}m\end{align*}
m in from of \begin{align*}m \angle ABC\end{align*}m∠ABC . — D. Ray  What you use to measure an angle. — E. Collinear
 When two sides of a triangle are congruent. — F. Perpendicular

\begin{align*}\bot\end{align*}
⊥ — G. Line  A line that passes through the midpoint of another line. — H. Protractor
 An angle that is greater than \begin{align*}90^\circ\end{align*}
90∘ . — I. Segment Addition Postulate  The intersection of two planes is a ___________. — J. Obtuse

\begin{align*}AB + BC = AC\end{align*}
AB+BC=AC — K. Point  An exact location in space. — L. \begin{align*}180^\circ\end{align*}
180∘  A sunbeam, for example. — M. Isosceles
 Every angle has exactly one. — N. Pentagon
 A closed figure with 5 sides. — O. Hexagon — P. Bisector
Texas Instruments Resources
In the CK12 Texas Instruments Geometry FlexBook, there are graphing calculator activities designed to supplement the objectives for some of the lessons in this chapter. See http://www.ck12.org/flexr/chapter/9686.
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