Geometry Chapter 4 Review Flashcards

Questions and Answers

What are congruent polygons?

Polygons that are similar

Polygons that have different side lengths

Polygons that have corresponding sides and angles congruent (correct)

Polygons that are not related

What does postulate 4-1: SSS state?

If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

What does postulate 4-2: SAS state?

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.

What does postulate 4-3: ASA 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 does theorem 4-2: AAS state?

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

What does CPCTC stand for?

Corresponding Parts of Congruent Triangles are Congruent. Signup and view all the answers

What does the isosceles triangle theorem state?

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

What does the converse of the isosceles triangle theorem state?

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

What does theorem 4-6: HL state?

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

What is the base of an isosceles triangle?

The non-congruent side; the side opposite the vertex angle. Signup and view all the answers

What is a corollary?

A special case of a theorem. Signup and view all the answers

What is the definition of 'hypotenuse'?

The side across from the 90 degree angle. Signup and view all the answers

What are the legs of a right triangle?

The two sides that form the right angle. Signup and view all the answers

What are the legs of an isosceles triangle?

The two equal sides. Signup and view all the answers

What is the vertex angle of an isosceles triangle?

The angle formed by the two equal sides. Signup and view all the answers

What does theorem 4-1 state?

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 postulate 4-1?

Side-Side-Side (SSS) Congruence; if three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent. Signup and view all the answers

What is postulate 4-2?

Side-Angle-Side (SAS) Congruence; 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 postulate 4-3?

Angle-Side-Angle (ASA) Congruence; 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 does theorem 4-3 state?

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

What happens once triangles are proven congruent?

Their corresponding parts (angles and sides) are congruent. Signup and view all the answers

CPCTC can be used before proving triangles congruent.

False Signup and view all the answers

What is the base angle of an isosceles triangle?

The angle formed by one base and one leg. Signup and view all the answers

What does theorem 4-5 state?

The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base. Signup and view all the answers

What is the corollary to theorem 4-3 regarding an equilateral triangle?

If a triangle is equilateral, then the triangle is equiangular. Signup and view all the answers

What is the corollary to theorem 4-4 regarding equiangular triangles?

If a triangle is equiangular, then the triangle is equilateral. Signup and view all the answers

What four things do you need to prove HL?

<ol> <li>Hypotenuse, 2) Legs, 3) Right angles, 4) Right triangles.</li> </ol> Signup and view all the answers

Study Notes

Congruent Polygons

Congruent polygons have corresponding sides and angles that are congruent.

Postulate 4-1: SSS (Side-Side-Side)

States that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Postulate 4-2: SAS (Side-Angle-Side)

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent.

Postulate 4-3: ASA (Angle-Side-Angle)

States that 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.

Theorem 4-2: AAS (Angle-Angle-Side)

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.

CPCTC

Corresponding Parts of Congruent Triangles are Congruent, used to prove congruence of segments and angles post triangle congruence.

Isosceles Triangle Theorem (4-3)

If two sides of a triangle are congruent, then the angles opposite those sides are also congruent.

Converse of the Isosceles Triangle Theorem (4-4)

States that if two angles of a triangle are congruent, then the sides opposite those angles are congruent.

Theorem 4-6: HL (Hypotenuse-Leg)

If the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent.

Base of an Isosceles Triangle

The non-congruent side of the isosceles triangle, opposite the vertex angle.

Corollary

A special case derived from a theorem.

Hypotenuse

The longest side of a right triangle, opposite the 90-degree angle.

Legs of a Right Triangle

The two sides that form the right angle.

Legs of an Isosceles Triangle

The two sides that are equal in length.

Vertex Angle of an Isosceles Triangle

The angle formed by the two equal sides of the triangle.

Theorem 4-1

If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. If the triangles are parallel, then the third angles are equal.

Using Congruent Triangles

Once triangles are proven congruent, all corresponding parts (angles and sides) are also congruent.

Base Angle of an Isosceles Triangle

Formed by one leg and one base of the triangle.

Theorem 4-5

The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base.

Corollary to Theorem 4-3

An equilateral triangle is also equiangular.

Corollary to Theorem 4-4

An equiangular triangle is also equilateral.

Requirements to Prove HL

Four criteria must be met: the hypotenuse, legs, right angles, and involvement of right triangles.

Studying That Suits You

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

Description

Test your knowledge with these flashcards focused on Chapter 4 of Geometry. Each card presents a key term or postulate related to congruent polygons and triangle congruence criteria. Perfect for reviewing essential concepts and definitions for your geometry studies.