Homework Help is Here – Start Your Trial Now!
Math
Geometry
Exercise 1 In earlier lessons, we have defined congruent to mean that there exists a sequence of rigid motions that maps one figure to the other. Congruent also means that all corresponding sides and angles are equal in measure. In order to prove triangles are congruent using their sides and angles (instead of using rigid motions), we do not need to prove all of their corresponding sides and angles are congruent. Instead we will look at criteria that refer to a few special groups of corresponding parts that will prove one triangle is congruent to another. We will start with: Side-Angle-Side Triangle Congruence Criteria (SAS) Triangles ABC and A'B'C' are marked below to show some corresponding parts are congruent. What parts are congruent? Notice that there is a sequence of rigid motions that maps AABC A'B'C' . Step 1: Translation Step 2: Rotation B' Step 3: Reflection B"" SIDE-ANGLE-SIDE (S.A.S.) THEOREM Two triangles are congruent if two sides and the included angle of one are equal (or congruent) to two sides and the included angle of the other.

Exercise 1 In earlier lessons, we have defined congruent to mean that there exists a sequence of rigid motions that maps one figure to the other. Congruent also means that all corresponding sides and angles are equal in measure. In order to prove triangles are congruent using their sides and angles (instead of using rigid motions), we do not need to prove all of their corresponding sides and angles are congruent. Instead we will look at criteria that refer to a few special groups of corresponding parts that will prove one triangle is congruent to another. We will start with: Side-Angle-Side Triangle Congruence Criteria (SAS) Triangles ABC and A'B'C' are marked below to show some corresponding parts are congruent. What parts are congruent? Notice that there is a sequence of rigid motions that maps AABC A'B'C' . Step 1: Translation Step 2: Rotation B' Step 3: Reflection B"" SIDE-ANGLE-SIDE (S.A.S.) THEOREM Two triangles are congruent if two sides and the included angle of one are equal (or congruent) to two sides and the included angle of the other.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
See similar textbooks
icon
Related questions
Topic Video
Question
Need help with the question
Exercise 1 In earlier lessons, we have defined congruent to mean that there exists a sequence of rigid motions that maps one figure to the other. Congruent also means that all corresponding sides and angles are equal in measure. In order to prove triangles are congruent using their sides and angles (instead of using rigid motions), we do not need to prove all of their corresponding sides and angles are congruent. Instead we will look at criteria that refer to a few special groups of corresponding parts that will prove one triangle is congruent to another. We will start with: Side-Angle-Side Triangle Congruence Criteria (SAS) Triangles ABC and A’B'C' are marked below to show some corresponding parts are congruent. What parts are congruent? Notice that there is a sequence of rigid motions that maps AABC=A'B'C' . Step 1: Translation Step 2: Rotation B' Step 3: Reflection B"" SIDE-ANGLE-SIDE (S.A.S.) THEOREM Two triangles are congruent if two sides and the included angle of one are equal (or congruent) to two sides and the included angle of the other.
Transcribed Image Text:Exercise 1 In earlier lessons, we have defined congruent to mean that there exists a sequence of rigid motions that maps one figure to the other. Congruent also means that all corresponding sides and angles are equal in measure. In order to prove triangles are congruent using their sides and angles (instead of using rigid motions), we do not need to prove all of their corresponding sides and angles are congruent. Instead we will look at criteria that refer to a few special groups of corresponding parts that will prove one triangle is congruent to another. We will start with: Side-Angle-Side Triangle Congruence Criteria (SAS) Triangles ABC and A’B'C' are marked below to show some corresponding parts are congruent. What parts are congruent? Notice that there is a sequence of rigid motions that maps AABC=A'B'C' . Step 1: Translation Step 2: Rotation B' Step 3: Reflection B"" SIDE-ANGLE-SIDE (S.A.S.) THEOREM Two triangles are congruent if two sides and the included angle of one are equal (or congruent) to two sides and the included angle of the other.
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Research Design Formulation
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS