Untitled Quiz

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?

Acute Triangle with all angles congruent Signup and view all the answers

What is a Scalene Triangle?

No two sides are congruent Signup and view all the answers

What distinguishes an Isosceles Triangle?

At least two sides are congruent Signup and view all the answers

What is an Equilateral Triangle?

All sides are congruent Signup and view all the answers

What is an Exterior Angle in a triangle?

Angle formed by one side and the extension of another Signup and view all the answers

What is a Remote Interior Angle?

Interior angles not adjacent to a given exterior angle Signup and view all the answers

What does it mean for triangles to be Congruent?

They are the same size and shape Signup and view all the answers

What does CPCTC stand for?

Congruent Parts of Congruent Triangles Signup and view all the answers

What is an Included Angle?

An angle formed by two adjacent sides Signup and view all the answers

What is an Included Side?

The side between two specific angles Signup and view all the answers

What does SSS stand for?

Side Side Side Signup and view all the answers

What does SAS stand for?

Side Angle Side Signup and view all the answers

What does ASA stand for?

Angle Side Angle Signup and view all the answers

What does AAS stand for?

Angle Angle Side Signup and view all the answers

What are Skew Lines?

Lines that do not intersect and are not coplanar Signup and view all the answers

What is a Transversal?

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

What is a Perpendicular Bisector?

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

What are Concurrent Lines?

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

What is a Point of Concurrency?

The point at which concurrent lines intersect Signup and view all the answers

What is a Circumcenter?

Point of concurrency of the perpendicular bisectors of a triangle Signup and view all the answers

What is an Incenter?

The point of concurrency in a triangle Signup and view all the answers

What is a Median in a triangle?

A segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side 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.