Unit 4: Congruent Triangles Vocabulary

Questions and Answers

What is a triangle?

A two-sided polygon

A four-sided polygon

A three-sided polygon (correct)

A five-sided polygon

Define a scalene triangle.

A triangle that has no congruent sides.

Define an isosceles triangle.

A triangle with two sides that are congruent.

Define an equilateral triangle.

A triangle where all three sides are congruent. Signup and view all the answers

What is an acute triangle?

A triangle where all of its angles measure less than 90 degrees. Signup and view all the answers

Define an obtuse triangle.

A triangle where one angle is obtuse and the other two are acute. Signup and view all the answers

What is a right triangle?

A triangle where one angle is a right angle. Signup and view all the answers

Define an equiangular triangle.

A triangle that has all congruent angles. Signup and view all the answers

What is the sum of the interior angles of a triangle?

180 degrees. Signup and view all the answers

Define the exterior angle theorem.

An exterior angle of a triangle has the measure of the sum of the two remote interior angles. Signup and view all the answers

What does the triangle sum theorem state?

The sum of the interior angles of a triangle is 180 degrees. Signup and view all the answers

Define congruent figures.

Figures that have the same size and shape. Signup and view all the answers

What are corresponding parts?

If two figures are congruent, then any pair of corresponding parts is congruent. Signup and view all the answers

Define the third angles theorem.

If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent. Signup and view all the answers

What is rigid motion or isometry?

Preserve length, measurements, and area. Signup and view all the answers

What are translations?

A slide; when an object slides a given distance in a given direction. Signup and view all the answers

Define reflections.

A flip, either over the x or y axis. Signup and view all the answers

What are rotations?

A spin around a given point. Signup and view all the answers

What does the Side-Side-Side Congruence Postulate (SSS) state?

If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. Signup and view all the answers

Define the hypotenuse of a right triangle.

The side of a right triangle opposite the right angle. Signup and view all the answers

What does the Angle-Side-Angle Congruence Postulate state?

If two angles and the included side are congruent to two angles and the included side of another triangle, then the triangles are congruent. Signup and view all the answers

State the Base Angles Theorem.

If two sides in a triangle are congruent, then the angles opposite to these sides are also congruent. Signup and view all the answers

What is a transformation?

Change in size or location. Signup and view all the answers

Define a congruence transformation.

A transformation that changes the position of a figure without changing its size or shape. Signup and view all the answers

Study Notes

Triangle Types

Triangle: A polygon with three sides.
Scalene Triangle: No sides are congruent.
Isosceles Triangle: Two sides are congruent.
Equilateral Triangle: All three sides are congruent.
Acute Triangle: All angles are less than 90 degrees.
Obtuse Triangle: One angle is obtuse (greater than 90 degrees).
Right Triangle: One angle is a right angle (90 degrees).
Equiangular Triangle: All angles are congruent.

Angle Properties

Interior Angles: Sum of the interior angles equals 180 degrees.
Exterior Angles: An angle formed outside of a triangle when one side is extended.
Triangle Sum Theorem: The sum of the interior angles of a triangle is always 180 degrees.
Exterior Angle Theorem: An exterior angle equals the sum of the two remote interior angles.
Corollary to Triangle Sum Theorem: In a right triangle, the acute angles are complementary (sum to 90 degrees).

Congruent Figures

Congruent Figures: Identical in shape and size.
Corresponding Parts: If figures are congruent, corresponding parts (sides and angles) are also congruent.
Third Angles Theorem: If two angles of one triangle are congruent to two angles of another triangle, the third angles are also congruent.

Congruence Postulates and Theorems

SSS (Side-Side-Side) Congruence Postulate: Triangles are congruent if all three sides match.
SAS (Side-Angle-Side) Congruence Postulate: Triangles are congruent if two sides and the included angle match.
Hypotenuse-Leg Theorem: Congruent hypotenuse and one leg of right triangles ensures triangle congruence.
Angle-Side-Angle Congruence Postulate: Triangles are congruent if two angles and the included side match.

Congruent Triangles and Transformations

CPCTC (Corresponding Parts of Congruent Triangles are Congruent): Corresponding parts of congruent triangles are congruent.
Base Angles Theorem: In an isosceles triangle, the angles opposite the congruent sides are also congruent.
Equilateral Triangle Properties: If a triangle is equilateral, it is also equiangular.

Transformations

Rigid Motion (Isometry): A transformation preserving lengths, angles, and area.
Translations: A slide where an object moves a specified distance in a specified direction.
Reflections: A flip over an axis (x-axis or y-axis).
Rotations: A spin around a specific point.

Coordinate Notation

Coordinate Notation for Translations: Specifies movements applied to points in the coordinate system.
Coordinate Notation for Reflections: Notation details how points change when reflected across axes.

Legs and Angles

Legs of a Right Triangle: The two sides that form the right angle.
Hypotenuse: The side opposite the right angle in a right triangle.
Legs of an Isosceles Triangle: The two congruent sides that define its shape.

Studying That Suits You

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Test your knowledge of congruent triangles with this vocabulary flashcard quiz. Learn the definitions of various types of triangles such as scalene, isosceles, and equilateral. Perfect for students looking to reinforce their understanding of triangle properties.