1.7: Chapter 1 Review
Symbol Toolbox
\begin{align*}\overleftrightarrow{AB}, \ \overrightarrow{AB}, \ \overline{AB}\end{align*} Line, ray, line segment
\begin{align*}\angle ABC\end{align*} Angle with vertex \begin{align*}B\end{align*}
\begin{align*}m \overline{AB} \ \text{or} \ AB\end{align*} Distance between \begin{align*}A\end{align*} and \begin{align*}B\end{align*}
\begin{align*}m \angle ABC\end{align*} Measure of \begin{align*}\angle ABC\end{align*}
\begin{align*}\bot\end{align*} Perpendicular
\begin{align*}=\end{align*} Equal
\begin{align*}\cong\end{align*} Congruent
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*}, \begin{align*}B\end{align*}, and \begin{align*}C\end{align*} are collinear and \begin{align*}B\end{align*} is between \begin{align*}A\end{align*} and \begin{align*}C\end{align*}, then \begin{align*}AB + BC = AC\end{align*}.
- 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*} and \begin{align*}180^\circ\end{align*} 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*}. The angle measure of a straight line.
- Right Angle
- When an angle measures \begin{align*}90^\circ\end{align*}.
- Acute Angles
- Angles that measure between \begin{align*}0^\circ\end{align*} and \begin{align*}90^\circ\end{align*}.
- Obtuse Angles
- Angles that measure between \begin{align*}90^\circ\end{align*} and \begin{align*}180^\circ\end{align*}.
- 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*} is on the interior of \begin{align*}\angle ADC\end{align*}, then \begin{align*}m \angle ADC = m \angle ADB + m \angle BDC\end{align*}.
- 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*}.
- Supplementary
- When two angles add up to \begin{align*}180^\circ\end{align*}.
- 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 non-common sides form a straight line.
- Linear Pair Postulate
- If two angles are a linear pair, then they are supplementary.
- Vertical Angles
- Two non-adjacent 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*} in from of \begin{align*}m \angle ABC\end{align*}. — 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*}. — I. Segment Addition Postulate
- The intersection of two planes is a ___________. — J. Obtuse
- \begin{align*}AB + BC = AC\end{align*} — K. Point
- An exact location in space. — L. \begin{align*}180^\circ\end{align*}
- 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 CK-12 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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