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Questions and Answers

What is an Acute Triangle?

  • One angle is obtuse
  • All angles equal 90 degrees
  • All angles less than 90 degrees (correct)
  • One angle is right

    • What characterizes an Obtuse Triangle?

  • No two sides are congruent
  • One angle is right
  • All angles less than 90 degrees
  • One angle is obtuse (correct)

    • What is a Right Triangle?

  • All angles equal 90 degrees
  • All angles less than 90 degrees
  • One angle is right (correct)
  • One angle is obtuse

    • What is an Equiangular Triangle?

    <p>Acute Triangle with all angles congruent</p> Signup and view all the answers

    What is a Scalene Triangle?

    <p>No two sides are congruent</p> Signup and view all the answers

    What distinguishes an Isosceles Triangle?

    <p>At least two sides are congruent</p> Signup and view all the answers

    What is an Equilateral Triangle?

    <p>All sides are congruent</p> Signup and view all the answers

    What is an Exterior Angle in a triangle?

    <p>Angle formed by one side and the extension of another</p> Signup and view all the answers

    What is a Remote Interior Angle?

    <p>Interior angles not adjacent to a given exterior angle</p> Signup and view all the answers

    What does it mean for triangles to be Congruent?

    <p>They are the same size and shape</p> Signup and view all the answers

    What does CPCTC stand for?

    <p>Congruent Parts of Congruent Triangles</p> Signup and view all the answers

    What is an Included Angle?

    <p>An angle formed by two adjacent sides</p> Signup and view all the answers

    What is an Included Side?

    <p>The side between two specific angles</p> Signup and view all the answers

    What does SSS stand for?

    <p>Side Side Side</p> Signup and view all the answers

    What does SAS stand for?

    <p>Side Angle Side</p> Signup and view all the answers

    What does ASA stand for?

    <p>Angle Side Angle</p> Signup and view all the answers

    What does AAS stand for?

    <p>Angle Angle Side</p> Signup and view all the answers

    What are Skew Lines?

    <p>Lines that do not intersect and are not coplanar</p> Signup and view all the answers

    What is a Transversal?

    <p>A line that intersects two or more lines in a plane at different points</p> Signup and view all the answers

    What is a Perpendicular Bisector?

    <p>A line that passes through the midpoint of a side and is perpendicular to that side</p> Signup and view all the answers

    What are Concurrent Lines?

    <p>Three or more lines that intersect at a common point</p> Signup and view all the answers

    What is a Point of Concurrency?

    <p>The point at which concurrent lines intersect</p> Signup and view all the answers

    What is a Circumcenter?

    <p>Point of concurrency of the perpendicular bisectors of a triangle</p> Signup and view all the answers

    What is an Incenter?

    <p>The point of concurrency in a triangle</p> Signup and view all the answers

    What is a Median in a triangle?

    <p>A segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side</p> Signup and view all the answers

    Study Notes

    Triangle Types

    • Acute Triangle: All angles measure less than 90 degrees.
    • Obtuse Triangle: Contains one angle greater than 90 degrees.
    • Right Triangle: Has one angle exactly equal to 90 degrees.
    • Equiangular Triangle: An acute triangle where all angles are congruent.
    • Scalene Triangle: No sides are congruent; all sides have different lengths.
    • Isosceles Triangle: At least two sides are congruent, often resulting in two equal angles.
    • Equilateral Triangle: All sides are congruent and all angles measure 60 degrees.

    Angle Relationships

    • Exterior Angle: Formed by one side of a triangle and the extension of an adjacent side.
    • Remote Interior Angle: Interior angles of a triangle that are not adjacent to a specific exterior angle.

    Triangle Congruence

    • Congruent Triangles: Triangles that have the same size and shape, which means corresponding parts are equal.
    • CPCTC: Stands for "Corresponding Parts of Congruent Triangles are Congruent."

    Triangle Properties

    • Included Angle: The angle formed between two sides of a triangle.
    • Included Side: The side that is between two given angles.

    Triangle Congruence Criteria

    • SSS (Side Side Side): Triangles are congruent if all three sides are equal.
    • SAS (Side Angle Side): Triangles are congruent if two sides and the included angle are equal.
    • ASA (Angle Side Angle): Triangles are congruent if two angles and the included side are equal.
    • AAS (Angle Angle Side): Triangles are congruent if two angles and a non-included side are equal.

    Line Relationships

    • Skew Lines: Lines that do not intersect and are not in the same plane.
    • Transversal: A line that crosses two or more lines at different points.

    Special Points in Triangles

    • Perpendicular Bisector: A line or segment that divides another segment at its midpoint at a right angle.
    • Concurrent Lines: Three or more lines that meet at a single point.
    • Point of Concurrency: The specific point where concurrent lines intersect.
    • Circumcenter: The point where the perpendicular bisectors of a triangle converge; equidistant from all triangle vertices.
    • Incenter: The point where the angle bisectors of a triangle converge; equidistant from all triangle sides.
    • Median: A line segment connecting a vertex of a triangle to the midpoint of the opposite side.

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