Glencoe Geometry Chapter 4 Flashcards

Questions and Answers

What defines an obtuse triangle?

A triangle with no congruent sides

A triangle with one right angle

A triangle with one obtuse angle (correct)

A triangle with 3 acute angles

What defines a right triangle?

A triangle with no congruent sides

A triangle with one obtuse angle

A triangle with 3 acute angles

A triangle with one right angle (correct)

What defines an acute triangle?

A triangle with 3 acute angles (correct)

A triangle with at least two congruent sides

A triangle with one obtuse angle

A triangle with one right angle

What defines a scalene triangle?

A triangle with no congruent sides Signup and view all the answers

What defines an isosceles triangle?

A triangle with at least two congruent sides Signup and view all the answers

What defines an equilateral triangle?

A triangle with 3 congruent angles Signup and view all the answers

What is an exterior angle?

The angle that is formed by extending one of the sides of a triangle Signup and view all the answers

What are remote interior angles?

The angles of a triangle that are nonadjacent to a given exterior angle Signup and view all the answers

What are congruent triangles?

Triangles that have the same size and shape Signup and view all the answers

What is an included angle?

An angle that is between two sides in a triangle Signup and view all the answers

What is an included side?

A side between two angles of a triangle Signup and view all the answers

What is the vertex angle in an isosceles triangle?

The angle between the two congruent sides Signup and view all the answers

What are the base angles in an isosceles triangle?

The angles opposite the two equal sides Signup and view all the answers

What is the SSS Postulate?

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

What is the SAS Postulate?

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

What is the ASA Postulate?

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

What is the AAS Theorem?

If two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. Signup and view all the answers

Study Notes

Triangle Definitions

Obtuse Triangle: Contains one angle that measures more than 90 degrees.
Right Triangle: Features one angle that measures exactly 90 degrees.
Acute Triangle: All three angles measure less than 90 degrees.
Scalene Triangle: No two sides are of equal length; all sides and angles are different.
Isosceles Triangle: At least two sides are of equal length; includes two equal angles.
Equilateral Triangle: All three sides are equal in length; each angle measures 60 degrees.
Equiangular Triangle: All angles are congruent, each measuring 60 degrees.

Triangle Angles

Exterior Angle: Formed by extending one side of the triangle outside the triangle, relative to the interior angles.
Remote Interior Angles: Angles inside the triangle that do not share a vertex with the exterior angle.

Congruence and Theorems

Congruent Triangles: Triangles that are identical in size and shape, matching all corresponding sides and angles.
Included Angle: The angle formed between two sides of a triangle.
Included Side: The side that lies between two given angles of a triangle.

Special Angles in Isosceles Triangles

Vertex Angle: The angle located between the two equal sides in an isosceles triangle.
Base Angles: The angles opposite the equal sides in an isosceles triangle.

Congruence Postulates and Theorems

SSS Postulate: States that if three sides of one triangle are congruent to three sides of another, the triangles are congruent.
SAS Postulate: States that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another, the triangles are congruent.
ASA Postulate: States that if two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
AAS Theorem: States that if two angles and a non-included side of one triangle are congruent to corresponding parts of another triangle, the triangles are congruent.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

Test your knowledge of triangles with these flashcards from Glencoe Geometry Chapter 4. Each card defines a different type of triangle, including obtuse, right, acute, scalene, and isosceles. Perfect for reinforcing your understanding of geometric concepts.