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1.7: Chapter 1 Review

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\overleftrightarrow{AB}, \ \overrightarrow{AB}, \ \overline{AB} Line, ray, line segment

\angle ABC Angle with vertex B

m \overline{AB} \ \text{or} \ AB Distance between A and B

m \angle ABC Measure of \angle ABC

\bot Perpendicular

= Equal

\cong 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 A, B, and C are collinear and B is between A and C, then 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 0^\circ and 180^\circ 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 180^\circ. The angle measure of a straight line.
Right Angle
When an angle measures 90^\circ.
Acute Angles
Angles that measure between 0^\circ and 90^\circ.
Obtuse Angles
Angles that measure between 90^\circ and 180^\circ.
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 B is on the interior of \angle ADC, then m \angle ADC = m \angle ADB + m \angle 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 90^\circ.
Supplementary
When two angles add up to 180^\circ.
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.

  1. When three points lie on the same line. — A. Measure
  2. All vertical angles are ________. — B. Congruent
  3. Linear pairs add up to _______. — C. Angle Bisector
  4. The m in from of m \angle ABC. — D. Ray
  5. What you use to measure an angle. — E. Collinear
  6. When two sides of a triangle are congruent. — F. Perpendicular
  7. \bot — G. Line
  8. A line that passes through the midpoint of another line. — H. Protractor
  9. An angle that is greater than 90^\circ. — I. Segment Addition Postulate
  10. The intersection of two planes is a ___________. — J. Obtuse
  11. AB + BC = AC — K. Point
  12. An exact location in space. — L. 180^\circ
  13. A sunbeam, for example. — M. Isosceles
  14. Every angle has exactly one. — N. Pentagon
  15. 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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