Geometry Triangle Properties Quiz

Questions and Answers

What is the Triangle Angle Sum Theorem?

The sum of the measures of the angles in a triangle is 180°.

What is an exterior angle of a triangle?

The angle formed by one side of a triangle and the extension of its adjacent side.

What are remote interior angles in a triangle?

The angles of a triangle that are not adjacent to the given exterior angle.

What does the Exterior Angle Theorem state?

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. Signup and view all the answers

What is a corollary?

A theorem that can be easily proved as a direct result of another theorem. Signup and view all the answers

Triangle angle sum corollary 4.1: The acute angles of a right triangle are _____________.

complementary Signup and view all the answers

Triangle angle sum corollary 4.2: There can be at most one right or _____________ angle in a triangle.

obtuse Signup and view all the answers

What are congruent polygons?

Polygons in which all pairs of corresponding parts (angles and sides) are congruent. Signup and view all the answers

What are corresponding parts?

Parts (angles or sides) that are in the same relative position in each of the figures. Signup and view all the answers

What does CPCTC stand for?

Corresponding parts of congruent triangles are congruent. Signup and view all the answers

What does the Third Angles Theorem state?

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

What is the Side Side Side (SSS) Congruence 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 an included angle?

An angle formed by two adjacent sides of a polygon. Signup and view all the answers

What does the Side Angle Side Congruence Postulate state?

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

What is an included side?

A side that is located between two consecutive angles. Signup and view all the answers

What does the Angle Side Angle (ASA) Congruence Postulate state?

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

What is the Angle Angle Side (AAS) Theorem?

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

What does Side Side Angle mean?

SSA does NOT guarantee that the triangles are congruent. Signup and view all the answers

What does Angle Angle Angle state?

AAA does NOT guarantee that the triangles are congruent. Signup and view all the answers

What is the Hypotenuse Leg (HL) Theorem?

If the hypotenuse and a leg of one triangle are congruent to the hypotenuse and corresponding leg of another triangle, then the triangles are congruent. Signup and view all the answers

What is an isosceles triangle?

A triangle that has at least two congruent sides. Signup and view all the answers

What are the legs of an isosceles triangle?

The congruent sides of an isosceles triangle. Signup and view all the answers

What is the vertex angle of an isosceles triangle?

The angle formed by the legs of an isosceles triangle. Signup and view all the answers

What is the base of an isosceles triangle?

The side opposite the vertex angle. Signup and view all the answers

What are the base angles of an isosceles triangle?

The two angles formed by the base and the congruent sides. Signup and view all the answers

What does the Isosceles Triangle Theorem state?

If two sides of one triangle are congruent, then the angles opposite those sides are congruent. Signup and view all the answers

What is the Converse of the Isosceles Triangle Theorem?

If two angles of a triangle are congruent, then the sides opposite those angles are congruent. Signup and view all the answers

What is an equilateral triangle?

A triangle with all sides congruent. Signup and view all the answers

Equilateral Triangle Corollary: A triangle is equilateral if and only if it is _________________.

equilangular Signup and view all the answers

Equilateral Triangle Corollary: Each angle of an equilateral triangle measures ______________.

60 degrees Signup and view all the answers

Study Notes

Triangle Properties

The Triangle Angle Sum Theorem states that the sum of angles in a triangle equals 180°.
An exterior angle of a triangle is formed by one triangle side and the extension of an adjacent side.
Remote interior angles are angles of a triangle that are not adjacent to a given exterior angle.
According to the Exterior Angle Theorem, an exterior angle of a triangle is equal to the sum of its two remote interior angles.

Angle Relationships and Theorems

A corollary is a theorem easily proven as a direct consequence of another theorem.
In a right triangle, the two acute angles are complementary (add up to 90°).
A triangle may contain at most one right angle or one obtuse angle.

Congruence in Polygons

Congruent polygons have all corresponding angles and sides congruent.
Corresponding parts are angles or sides in the same position across figures.
CPCTC (Corresponding Parts of Congruent Triangles are Congruent) is essential for proving triangle congruence.

Triangle Congruence Theorems

The Third Angles Theorem states if two angles in one triangle are congruent to two angles in another, then the third angles are also congruent.
SSS Congruence Postulate asserts that triangles are congruent if all three sides are congruent.
The Side Angle Side (SAS) Congruence Postulate indicates triangles are congruent if two sides and the included angle match in both triangles.
The Angle Side Angle (ASA) Congruence Postulate applies when two angles and the included side of one triangle are congruent to the other triangle.
The Angle Angle Side (AAS) Theorem states congruence when two angles and the nonincluded side of one triangle match the corresponding parts of another triangle.

Limitations of Congruence Criteria

Side Side Angle (SSA) does not guarantee triangle congruence.
Angle Angle Angle (AAA) does not imply congruence either.

Unique Case for Right Triangles

The Hypotenuse Leg (HL) Theorem confirms congruence in right triangles when the hypotenuse and one leg are congruent to those in another triangle.

Isosceles Triangle Properties

An isosceles triangle has at least two congruent sides.
The legs of an isosceles triangle are the two congruent sides.
The vertex angle is the angle formed by the two legs of the isosceles triangle.
The base is the side opposite to the vertex angle.
Base angles are the two angles formed between the base and the legs.

Isosceles Triangle Theorems

The Isosceles Triangle Theorem states that if two sides are congruent, the angles opposite those sides are also congruent.
The Converse of the Isosceles Triangle Theorem indicates that if two angles are congruent, the sides opposite those angles are congruent.

Special Triangle Types

An equilateral triangle has all sides congruent.
An equilateral triangle is also equilangular, meaning all angles are equal.
Each angle in an equilateral triangle measures 60 degrees.

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Description

Test your knowledge of triangle properties and theorems with this quiz. Explore concepts such as the Triangle Angle Sum Theorem, exterior angles, and the relationships between angles in triangles. Challenge yourself with questions on congruence and related theorems.