Moise/Downs Geometry Chapter 9 Flashcards
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Questions and Answers

What are skew lines?

  • Lines that are parallel
  • Lines that intersect
  • Lines that are coplanar
  • Lines that don't lie in the same plane (correct)

    • Parallel lines must always intersect.

    False

    What is Theorem 9-1?

    Two parallel lines lie in exactly one plane.

    What does Theorem 9-2 state?

    <p>If two lines are both perpendicular to the same line, then they are parallel.</p> Signup and view all the answers

    What is the existence of parallels?

    <p>Let L be a line and let P be a point not on L. There is at least one line through P, parallel to L.</p> Signup and view all the answers

    What is a transversal?

    <p>A line which intersects two coplanar lines at two different points.</p> Signup and view all the answers

    What are alternate interior angles?

    <p>Angles defined by the figure and positioning of lines cut by a transversal.</p> Signup and view all the answers

    What is Theorem 9-4?

    <p>If two lines are cut by a transversal, and one pair of alternate interior angles are congruent, then the other pair of alternate interior angles are also congruent.</p> Signup and view all the answers

    What does AIP stand for?

    <p>Given two lines cut by a transversal. If a pair of alternate interior angles are congruent, then the lines are parallel.</p> Signup and view all the answers

    What are corresponding angles?

    <p>[Answer not provided in content]</p> Signup and view all the answers

    What are same-side interior angles?

    <p>[Answer not provided in content]</p> Signup and view all the answers

    What does CAAI stand for?

    <p>Given two lines cut by a transversal. If a pair of corresponding angles are congruent, then a pair of alternate interior angles are congruent.</p> Signup and view all the answers

    What does CAP stand for?

    <p>Given two lines cut by a transversal. If a pair of corresponding angles are congruent, then the lines are parallel.</p> Signup and view all the answers

    What does SSSP stand for?

    <p>Given two lines cut by a transversal. If a pair of same-side interior angles are supplementary, then the lines are parallel.</p> Signup and view all the answers

    What is the Parallel Postulate?

    <p>Through a given external point, there is only one parallel to a given line.</p> Signup and view all the answers

    What does PAI state?

    <p>If two parallel lines are cut by a transversal, then alternate interior angles are congruent.</p> Signup and view all the answers

    What does PCA state?

    <p>If two parallel lines are cut by a transversal, each pair of corresponding angles are congruent.</p> Signup and view all the answers

    What does PSSS state?

    <p>If two parallel lines are cut by a transversal, the two pairs of same-side interior angles are supplementary.</p> Signup and view all the answers

    What is Theorem 9-10?

    <p>In a plane, if a line intersects one of two parallel lines in only one point, then it intersects the other.</p> Signup and view all the answers

    What is Parallel Transitivity?

    <p>In a plane, if two lines are each parallel to a third line, then they are parallel to each other.</p> Signup and view all the answers

    What is Perpendicular Transitivity?

    <p>In a plane, if a line is perpendicular to one of two parallel lines, it is perpendicular to the other.</p> Signup and view all the answers

    What is Triangle Angle Sum?

    <p>For every triangle, the sum of the measures of the angles is 180.</p> Signup and view all the answers

    What does Convex Quadrilateral describe?

    <p>A quadrilateral where no two of its vertices lie on opposite sides of the line containing a side of the quadrilateral.</p> Signup and view all the answers

    What is a Parallelogram?

    <p>A quadrilateral where both pairs of opposite sides are parallel.</p> Signup and view all the answers

    What is a Trapezoid?

    <p>A quadrilateral where only one pair of opposite sides are parallel.</p> Signup and view all the answers

    What are the bases of a trapezoid?

    <p>The parallel sides of a trapezoid.</p> Signup and view all the answers

    What is the median of a trapezoid?

    <p>Segment formed by the midpoints of the two non-parallel sides of a trapezoid.</p> Signup and view all the answers

    What does the Midline Theorem state?

    <p>The segment between midpoints of two sides of a triangle is parallel to the third side and half as long.</p> Signup and view all the answers

    What is the Quadrilateral Midpoint Theorem?

    <p>The midpoints of the sides of any quadrilateral form a parallelogram.</p> Signup and view all the answers

    What does the Isosceles Trapezoid Theorem state?

    <p>The base angles of an isosceles trapezoid are congruent.</p> Signup and view all the answers

    What is a Rhombus?

    <p>A parallelogram all of whose sides are congruent.</p> Signup and view all the answers

    What is a Rectangle?

    <p>A parallelogram all of whose angles are right angles.</p> Signup and view all the answers

    What is a Square?

    <p>A rectangle all of whose sides are congruent.</p> Signup and view all the answers

    What does it mean if a parallelogram has one right angle?

    <p>Then it has four right angles, and the parallelogram is a rectangle.</p> Signup and view all the answers

    What is true about the diagonals of a rhombus?

    <p>The diagonals are perpendicular to one another.</p> Signup and view all the answers

    What can be concluded if the diagonals of a quadrilateral bisect each other and are perpendicular?

    <p>Then the quadrilateral is a rhombus.</p> Signup and view all the answers

    What is the median to the hypotenuse of a right triangle?

    <p>Half as long as the hypotenuse.</p> Signup and view all the answers

    What does the converse of 30-60-90 imply?

    <p>If one leg of a right triangle is half as long as the hypotenuse, then the opposite angle has measure 30.</p> Signup and view all the answers

    What does Theorem 9-29 state?

    <p>If three parallel lines intercept congruent segments on transversal T, then they intercept congruent segments on any transversal T' parallel to T.</p> Signup and view all the answers

    What does Theorem 9-30 state?

    <p>If three parallel lines intercept congruent segments on one transversal, then they intercept congruent segments on any other transversal.</p> Signup and view all the answers

    What does TMPT state?

    <p>If three or more parallel lines intercept congruent segments on one transversal, then they intercept congruent segments on any other transversal.</p> Signup and view all the answers

    Study Notes

    Lines and Angles

    • Skew Lines are non-coplanar and do not intersect.
    • Parallel Lines are coplanar and do not intersect.
    • Theorem 9-1 states two parallel lines lie within exactly one plane.
    • Theorem 9-2 asserts that if two lines are both perpendicular to the same line in a plane, they are parallel.

    Parallels and Transversals

    • At least one line through point P exists that is parallel to line L if P is not on L.
    • Transversal is a line intersecting two coplanar lines at two distinct points.
    • Alternate Interior Angles (AIA) are formed when a transversal intersects two lines, creating angles that are on opposite sides of the transversal and inside the lines.
    • Theorem 9-4 indicates that if a pair of alternate interior angles are congruent, then the other pair will also be congruent.
    • If a pair of alternate interior angles are congruent, the lines cut by the transversal are parallel.

    Angle Relationships

    • Corresponding Angles - angles that occupy the same relative position at each intersection.
    • Same-Side Interior Angles - interior angles on the same side of the transversal.
    • CAAI suggests that if corresponding angles are congruent, then alternate interior angles are also congruent.
    • CAP states if corresponding angles are congruent, the lines are parallel.
    • SSSP indicates that if same-side interior angles are supplementary, the lines are parallel.

    Postulates and Properties

    • Parallel Postulate states through a given point outside a line, only one parallel line exists to that line.
    • PAI states alternate interior angles of parallel lines cut by a transversal are congruent.
    • PCA indicates correspondence in angles for parallel lines cut by a transversal.
    • PSSS asserts that two pairs of same side interior angles in a parallelogram are supplementary.

    Geometry of Parallelograms

    • Theorem 9-10 declares if a line intersects one of two parallel lines at one point, it will intersect the other as well.
    • Parallel Transitivity: If two lines are each parallel to a third line, they are parallel to each other.
    • Perpendicular Transitivity: A line perpendicular to one of two parallel lines is perpendicular to the other.
    • The Triangle Angle Sum states the total angle measures in any triangle equate to 180 degrees.

    Quadrilaterals

    • Convex Quadrilateral: no vertices lie on opposite sides of any line that extends a side.
    • Parallelogram: quadrilateral where both pairs of opposite sides are parallel.
    • Trapezoid: quadrilateral with one pair of parallel sides (the bases).
    • Median of Trapezoid: segment connecting midpoints of non-parallel sides is parallel to the base and half its length.

    Properties of Parallelograms

    • Diagonals bisect each other, and opposite sides are congruent.
    • Opposite angles within a parallelogram are congruent; consecutive angles are supplementary.
    • If both pairs of opposite sides or angles are congruent, or if the diagonals bisect each other, the quadrilateral is a parallelogram.

    Special Types of Quadrilaterals

    • Rhombus: all sides congruent; diagonals perpendicular.
    • Rectangle: all angles are right angles.
    • Square: a rectangle with all sides congruent.
    • If a parallelogram has one right angle, it contains four right angles.

    Triangles and Angles

    • Midline Theorem: mid-segment in a triangle is parallel to the base and half its length.
    • Isosceles Trapezoid Theorem states the base angles of an isosceles trapezoid are congruent.
    • In any triangle, the measure of an exterior angle is equal to the sum of the two remote interior angles.
    • Theorem 9-29: if three parallel lines intercept congruent segments on one transversal, they intercept congruent segments on any parallel transversal.
    • Theorem 9-30: three parallel lines intercept congruent segments on one transversal will do so on any transversal.

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    Description

    Test your knowledge on the key concepts from Chapter 9 of Moise and Downs' Geometry. This quiz covers essential definitions and theorems regarding lines, including skew and parallel lines, and their properties in a plane. Perfect for students looking to reinforce their understanding of geometric principles.

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