Triangle congruence by SSS and SAS practice 4 2 introduces the fundamental concepts of triangle congruence and provides a comprehensive set of practice problems to enhance your understanding. This guide will delve into the definitions of SSS (Side-Side-Side) and SAS (Side-Angle-Side) congruence, followed by step-by-step solutions and illustrative diagrams to reinforce your learning.

Through this practice, you will gain proficiency in identifying and applying the congruence criteria, solidifying your understanding of triangle geometry.

Triangle Congruence by SSS and SAS

Triangle congruence is a fundamental concept in geometry that establishes when two triangles have the same shape and size. This property allows for the identification and comparison of triangles, providing valuable insights into their geometric relationships.

Two specific criteria for triangle congruence are the Side-Side-Side (SSS) and Side-Angle-Side (SAS) congruence properties. These criteria provide conditions under which triangles can be proven congruent.

SSS Congruence

• Definition:Two triangles are congruent by SSS if the corresponding sides of the triangles are equal in length.
• Theorem:If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

SAS Congruence

• Definition:Two triangles are congruent by SAS if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.
• Theorem: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.

Practice Problems, Triangle congruence by sss and sas practice 4 2

SSS Congruence

1. Given a triangle with sides 5 cm, 7 cm, and 9 cm, find another triangle that is congruent to it.
2. Prove that two triangles are congruent if their sides measure 3 cm, 4 cm, and 5 cm, and 5 cm, 4 cm, and 3 cm, respectively.
3. Determine if the triangles with sides 2 cm, 3 cm, and 4 cm, and 3 cm, 4 cm, and 2 cm are congruent.
4. Find the missing side length of a triangle if two sides measure 6 cm and 8 cm, and the third side is congruent to the first side.

SAS Congruence

1. Given a triangle with sides 5 cm, 7 cm, and an angle of 60 degrees, find another triangle that is congruent to it.
2. Prove that two triangles are congruent if their sides measure 3 cm, 4 cm, and 5 cm, and one of the triangles has an angle of 60 degrees and the other has an angle of 30 degrees.
3. Determine if the triangles with sides 2 cm, 3 cm, and an angle of 45 degrees, and 3 cm, 2 cm, and an angle of 45 degrees are congruent.
4. Find the missing angle measure of a triangle if two sides measure 6 cm and 8 cm, and one of the angles is 30 degrees.

Step-by-Step Solutions

[Isi dengan solusi untuk masalah latihan]

Examples with Diagrams

[Isi dengan diagram untuk mengilustrasikan sifat kongruensi SSS dan SAS]

Table of Congruence Criteria

Congruence Property	Theorem	Explanation
SSS Congruence	If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.	The corresponding sides of the triangles have the same length.
SAS Congruence	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.	The corresponding sides and the included angles of the triangles have the same measure.

Expert Answers: Triangle Congruence By Sss And Sas Practice 4 2

What is triangle congruence?

Triangle congruence is a property where two triangles have the same shape and size, meaning their corresponding sides and angles are equal.

What is SSS congruence?

SSS congruence is a congruence criterion that states that if the three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.

What is SAS congruence?

SAS congruence is a congruence criterion that states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.