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Honors Geometry 1.1 1.2 review

Geo hon 1.1 1.2
Course

Geometry (MTG 3212)

3 Documents
Students shared 3 documents in this course
Academic year: 2022/2023
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University of Florida

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Section 1 Basics of Geometry

Undefined Terms-terms that are needed to define all other terms. Point, line, and plane are examples.

Point: point A Line: Plane: EFG, FGE, FEG, or P Defined Terms

line segment

vertex B(Vertices plural). ∠B, ∠ABC, ∠CBA. Parallel:

a || b

Perpendicular: c ⊥ d. circle P or ⊙P

Postulates vs Theorems: Postulate: a known fact Theorem: information that seems true but must be proven Points Postulate—Through any two points, there is exactly one line. Intersecting Lines Postulate—If two lines intersect, then they intersect in exactly one point. Intersecting Planes Postulate—If two distinct planes intersect, then they intersect in exactly one line. Coplanar Points Postulate—Through any three non-collinear points, there is exactly one plane.

Segment Addition Postulate—If B is between A and C, then Angle Addition Postulate—If S is in the interior of ∠PQR, then m∠PQS + m∠SQR = m∠PQR. Linear Pair Postulate—Two angles that form a linear pair are supplementary.

Vertical Angles Theorem —Vertical angles are congruent. Corresponding Angles Theorem—If a transversal intersects two parallel lines, then corresponding angles are congruent. Alternate Interior Angles Theorem—If a transversal intersects two parallel lines, then alternate interior angles are congruent. Alternate Exterior Angles Theorem—Exterior angles are congruent. Same-Side Interior Angles Theorem—If a transversal intersects two parallel lines, then same-side interior angles are supplementary.

1 Basic Constructions

  1. congruent: all same measurements ≅,means "congruent to." AB ≅ CD. hash marks are different, not congruent

  2. arc: part of the circumference of a circle

  3. segment bisector: a line, point, segment, or ray that divides a segment into two equal pieces

  4. midpoint: a point that divides a segment into two congruent segments

  5. perpendicular bisector: a line that is perpendicular to a segment at its mid-

point. 6. acute angle: an angle that measures less than 90 degrees 7. obtuse angle: an angle that measures > 90 degrees but < 180 degrees 8. right angle: an angle that measures exactly 90 degrees: little square at the vertex 9. straight angle: an angle that measures 180 degrees 10. inscribed polygon: a polygon that is inside the circle so that the vertices(cor- ners) of the shape touch the circle but never pass outside the circle 11. regular polygon: all sides are congruent and all interior angles have the same measure

Straightedge: to connect the endpoints Compass: to create the accurate distance between the two endpoints_

Steps for constructing a line segment: 1. You are given a segment with two endpoints. 2. Draw a ray with one endpoint that is longer than the given segment. 3. Open the compass to the width of the given segment. 4. Place the compass on the ray's endpoint, and swing an arc that intersects the ray. 5. The intersection point of the ray and the arc is the second endpoint that makes the new line segment congruent to the given one.

To copy a segment using technology, follow these steps:

● Create segment AB. ● Draw point C. ● Create circle C with the same radius as segment AB. ● Draw point D on circle C. ● Connect points C and D with a segment. ● Segment CD is a copy of segment AB. Bisecting a Segment

  1. You are given a segment with two endpoints.
  2. Place the compass on one of the endpoints, and open the compass to a distance more than halfway across the segment(if less than, circles A and B would not have intersected).
  3. Swing an arc on either side of the segment.
  4. Keeping the compass at the same width, place the compass on the other endpoint and swing arcs on either side so that they intersect the first two arcs created.
  5. Mark the intersection points of the arcs, and draw a line through those two points.
  6. The point where this new line crosses the given segment is the midpoint and divides the segment in half.
  7. When you bisect a segment, you also construct a perpendicular bisector.

● Straight angles are lines or line segments, and the measurement is 180°. ● Acute angles are angles that measure less than 90°. ● Obtuse angles are angles that measure more than 90°, but less than 180°. ● Right angles are angles that measure exactly 90°.

Bisecting an Angle ● You are given an angle. ● Place the compass on the vertex of the angle. ● Swing an arc that intersects both rays of the angle. ● Mark the intersection points of the rays and the arc. ● Place the compass on one of those intersection points, and draw an arc inside the angle. ● Keeping the compass at the same width, place the compass on the second intersection point and swing an arc that intersects the first. ● Mark the intersection point of the two arcs, and draw a ray from the vertex through this intersection point. To bisect an angle using technology, follow these steps: ● Create ray AB. ● Create ray AC. ● Create point D on segment AB. ● Create circle A with radius AD. ● Mark the point of intersection between circle A and ray AC. Label this point E. ● Create circles D and E with radii equal in length to the distance between points D and C. ● Mark the points of intersection between circles D and E. Label these points F and G. ● Create line FG. ● Line FG bisects ∡BAC.

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Honors Geometry 1.1 1.2 review

Course: Geometry (MTG 3212)

3 Documents
Students shared 3 documents in this course

University: University of Florida

Was this document helpful?
1
Section 1.01 Basics of Geometry
Undefined Terms-terms that are needed to define all other terms. Point,
line, and plane are examples.
Point: point A Line: Plane: EFG, FGE, FEG, or P
Defined Terms
line segment
vertex B(Vertices plural). ∠B, ∠ABC, ∠CBA. Parallel:
a || b
Perpendicular: c ⊥ d. circle P or ⊙P
Postulates vs Theorems:
Postulate: a known fact Theorem: information that seems true
but must be proven
Points Postulate—Through any two points, there is exactly one line.
Intersecting Lines Postulate—If two lines intersect, then they intersect in exactly
one point.
Intersecting Planes Postulate—If two distinct planes intersect, then they
intersect in exactly one line.
Coplanar Points Postulate—Through any three non-collinear points, there is
exactly one plane.
Segment Addition Postulate—If B is between A and C, then
Angle Addition Postulate—If S is in the interior of ∠PQR, then m∠PQS + m∠SQR
= m∠PQR.
Linear Pair Postulate—Two angles that form a linear pair are supplementary.
Vertical Angles Theorem —Vertical angles are congruent.
Corresponding Angles Theorem—If a transversal intersects two parallel lines,
then corresponding angles are congruent.
Alternate Interior Angles Theorem—If a transversal intersects two parallel lines,
then alternate interior angles are congruent.
Alternate Exterior Angles Theorem—Exterior angles are congruent.
Same-Side Interior Angles Theorem—If a transversal intersects two parallel
lines, then same-side interior angles are supplementary.
1.02 Basic Constructions
1. congruent: all same measurements ≅,means "congruent to."
AB ≅ CD. hash marks are different, not congruent
2. arc: part of the circumference of a circle
3. segment bisector: a line, point, segment, or ray that divides a segment into
two equal pieces
4. midpoint: a point that divides a segment into two congruent segments

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