4.1 Apply Congruence and Triangles 4.2 Prove Triangles Congruent by SSS, SAS Objectives: 1. To...

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4.1 Apply Congruence and Triangles 4.2 Prove Triangles Congruent by SSS, SAS Objectives: 1. To define congruent triangles 2. To write a congruent statement 3. To prove triangles congruent by SSS, SAS

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Transcript of 4.1 Apply Congruence and Triangles 4.2 Prove Triangles Congruent by SSS, SAS Objectives: 1. To...

Page 1: 4.1 Apply Congruence and Triangles 4.2 Prove Triangles Congruent by SSS, SAS Objectives: 1. To define congruent triangles 2. To write a congruent statement.

4.1 Apply Congruence and Triangles4.2 Prove Triangles Congruent by SSS, SAS

Objectives:1. To define congruent triangles2. To write a congruent statement3. To prove triangles congruent by SSS,

SAS

Page 2: 4.1 Apply Congruence and Triangles 4.2 Prove Triangles Congruent by SSS, SAS Objectives: 1. To define congruent triangles 2. To write a congruent statement.

Congruent Polygons

Page 3: 4.1 Apply Congruence and Triangles 4.2 Prove Triangles Congruent by SSS, SAS Objectives: 1. To define congruent triangles 2. To write a congruent statement.

Congruent Triangles (CPCTC)

Two triangles are congruent congruent triangles triangles if and only if the ccorresponding pparts of those ccongruent ttriangles are ccongruent.

• Corresponding sides are congruent

• Corresponding angles are congruent

Page 4: 4.1 Apply Congruence and Triangles 4.2 Prove Triangles Congruent by SSS, SAS Objectives: 1. To define congruent triangles 2. To write a congruent statement.

Congruence Statement

When naming two congruent triangles, order is very important.

Page 5: 4.1 Apply Congruence and Triangles 4.2 Prove Triangles Congruent by SSS, SAS Objectives: 1. To define congruent triangles 2. To write a congruent statement.

Example

Write a congruence statement for the congruent triangles below.

Page 6: 4.1 Apply Congruence and Triangles 4.2 Prove Triangles Congruent by SSS, SAS Objectives: 1. To define congruent triangles 2. To write a congruent statement.

Example

Which polygon is congruent to ABCDE?ABCDE -?-

Page 7: 4.1 Apply Congruence and Triangles 4.2 Prove Triangles Congruent by SSS, SAS Objectives: 1. To define congruent triangles 2. To write a congruent statement.

Properties of Congruent Triangles

Page 8: 4.1 Apply Congruence and Triangles 4.2 Prove Triangles Congruent by SSS, SAS Objectives: 1. To define congruent triangles 2. To write a congruent statement.

Example

What is the relationship between C and F?

30

30

75

75

E

F

D

A

C

B

Page 9: 4.1 Apply Congruence and Triangles 4.2 Prove Triangles Congruent by SSS, SAS Objectives: 1. To define congruent triangles 2. To write a congruent statement.

Third Angle Theorem

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

Page 10: 4.1 Apply Congruence and Triangles 4.2 Prove Triangles Congruent by SSS, SAS Objectives: 1. To define congruent triangles 2. To write a congruent statement.

Congruent Triangles

Checking to see if 3 pairs of corresponding sides are congruent and then to see if 3 pairs of corresponding angles are congruent makes a total of SIX pairs of things, which is a lot! Surely there’s a shorter way!

Page 11: 4.1 Apply Congruence and Triangles 4.2 Prove Triangles Congruent by SSS, SAS Objectives: 1. To define congruent triangles 2. To write a congruent statement.

Congruence Shortcuts?

Will one pair of congruent sides be sufficient? One pair of angles?

Page 12: 4.1 Apply Congruence and Triangles 4.2 Prove Triangles Congruent by SSS, SAS Objectives: 1. To define congruent triangles 2. To write a congruent statement.

Congruence Shortcuts?

Will two congruent parts be sufficient?

Page 13: 4.1 Apply Congruence and Triangles 4.2 Prove Triangles Congruent by SSS, SAS Objectives: 1. To define congruent triangles 2. To write a congruent statement.

Congruent Shortcuts?

Will three congruent parts be sufficient?

And if so….what three parts?

Page 14: 4.1 Apply Congruence and Triangles 4.2 Prove Triangles Congruent by SSS, SAS Objectives: 1. To define congruent triangles 2. To write a congruent statement.

Investigation…

… Using 2,3,4 Triangles

Page 15: 4.1 Apply Congruence and Triangles 4.2 Prove Triangles Congruent by SSS, SAS Objectives: 1. To define congruent triangles 2. To write a congruent statement.

Side-Side-Side Congruence Postulate

SSS Congruence Postulate:SSS Congruence Postulate:If the three sides of one triangle are

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

Page 16: 4.1 Apply Congruence and Triangles 4.2 Prove Triangles Congruent by SSS, SAS Objectives: 1. To define congruent triangles 2. To write a congruent statement.

SSS Congruence Postulate

Page 17: 4.1 Apply Congruence and Triangles 4.2 Prove Triangles Congruent by SSS, SAS Objectives: 1. To define congruent triangles 2. To write a congruent statement.

A B

C

D

Using a 2-Column Proof!

Is ABC is congruent to ABD? Why or why not?

Page 18: 4.1 Apply Congruence and Triangles 4.2 Prove Triangles Congruent by SSS, SAS Objectives: 1. To define congruent triangles 2. To write a congruent statement.

Example

Decide whether the triangles are congruent. Explain your reasoning.

Page 19: 4.1 Apply Congruence and Triangles 4.2 Prove Triangles Congruent by SSS, SAS Objectives: 1. To define congruent triangles 2. To write a congruent statement.

Investigation…

…

Part 2

Page 20: 4.1 Apply Congruence and Triangles 4.2 Prove Triangles Congruent by SSS, SAS Objectives: 1. To define congruent triangles 2. To write a congruent statement.

Congruence Shortcuts

Side-Angle-Side (SAS) Congruence Side-Angle-Side (SAS) Congruence Postulate: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 two triangles are congruent.

Page 21: 4.1 Apply Congruence and Triangles 4.2 Prove Triangles Congruent by SSS, SAS Objectives: 1. To define congruent triangles 2. To write a congruent statement.

Can we prove?...yet?

Page 22: 4.1 Apply Congruence and Triangles 4.2 Prove Triangles Congruent by SSS, SAS Objectives: 1. To define congruent triangles 2. To write a congruent statement.

What else would we need?

Page 23: 4.1 Apply Congruence and Triangles 4.2 Prove Triangles Congruent by SSS, SAS Objectives: 1. To define congruent triangles 2. To write a congruent statement.

Can we Prove Triangle Congruence?

Page 24: 4.1 Apply Congruence and Triangles 4.2 Prove Triangles Congruent by SSS, SAS Objectives: 1. To define congruent triangles 2. To write a congruent statement.

Another Proof…?

Page 25: 4.1 Apply Congruence and Triangles 4.2 Prove Triangles Congruent by SSS, SAS Objectives: 1. To define congruent triangles 2. To write a congruent statement.

Classwork

From 4.13 - 1232 – 3538 – 4046 – 48*

From 4.21 - 48 - 1722 - 3041 - 42


Then/Now You proved whether two triangles were congruent. Identify reflections, translations, and rotations. Verify congruence after a congruence transformation.

Then/Now You proved whether two triangles were congruent. Identify reflections, translations, and rotations. Verify congruence after a congruence transformation.

CONGRUENCE AND SIMILARITY - Amazon S3 · CONGRUENCE AND SIMILARITY ... Two triangles are congruent if Two Angles and a Corresponding Sides are equal . ... 1.2 CONGRUENCE AND TRANSFORMATION

CONGRUENCE AND SIMILARITY - Amazon S3 · CONGRUENCE AND SIMILARITY ... Two triangles are congruent if Two Angles and a Corresponding Sides are equal . ... 1.2 CONGRUENCE AND TRANSFORMATION

& CONGRUENT TRIANGLES NCSCOS: 2.02; 2.03 U.E.Q: How do we prove the congruence of triangles, and how do we use the congruence of triangles solving real-life.

& CONGRUENT TRIANGLES NCSCOS: 2.02; 2.03 U.E.Q: How do we prove the congruence of triangles, and how do we use the congruence of triangles solving real-life.

Congruence of Triangles - 8th Grade Mathchmsmath8.weebly.com/uploads/1/6/2/5/16253668/student_text_cha… · 8.2 Congruent Triangles • 441 All the Same to You Congruent Triangles

Congruence of Triangles - 8th Grade Mathchmsmath8.weebly.com/uploads/1/6/2/5/16253668/student_text_cha… · 8.2 Congruent Triangles • 441 All the Same to You Congruent Triangles

4.2 CONGRUENT FIGURES - Mathematics with Mr. Thoreson€¦ · CHAPTER 4 Triangles and Congruence Chapter Outline 4.1 TRIANGLE SUMS 4.2 CONGRUENT FIGURES 4.3 TRIANGLE CONGRUENCE USING

4.2 CONGRUENT FIGURES - Mathematics with Mr. Thoreson€¦ · CHAPTER 4 Triangles and Congruence Chapter Outline 4.1 TRIANGLE SUMS 4.2 CONGRUENT FIGURES 4.3 TRIANGLE CONGRUENCE USING

Congruence with Multiple Sides · congruent, but the corresponding sides are not congruent . So, knowing that two triangles have three corresponding congruent angles is not enough

Congruence with Multiple Sides · congruent, but the corresponding sides are not congruent . So, knowing that two triangles have three corresponding congruent angles is not enough

ASA- Angle Side Angle Used to prove triangle congruence: if two angles and the included side of two triangles are congruent, then the triangles are congruent.

ASA- Angle Side Angle Used to prove triangle congruence: if two angles and the included side of two triangles are congruent, then the triangles are congruent.

7-3 Similar Triangles You used the AAS, SSS, and SAS Congruence Theorems to prove triangles congruent. Identify similar triangles using the AA Similarity.

7-3 Similar Triangles You used the AAS, SSS, and SAS Congruence Theorems to prove triangles congruent. Identify similar triangles using the AA Similarity.

kimgaringermath.weebly.comkimgaringermath.weebly.com/uploads/8/6/...triangles... · According to the RHS criterion of congruence, two right angles triangles are said to be congruent

kimgaringermath.weebly.comkimgaringermath.weebly.com/uploads/8/6/...triangles... · According to the RHS criterion of congruence, two right angles triangles are said to be congruent

Loudoun County Public Schools...4.3-4.5 Prove Triangles congruent Objective. Proving triangles congruent by triangle congruence theorems Side-Side-Side (SSS) Congruence Postulate If

Loudoun County Public Schools...4.3-4.5 Prove Triangles congruent Objective. Proving triangles congruent by triangle congruence theorems Side-Side-Side (SSS) Congruence Postulate If

Unit 2: Congruence, Similarity, and Proofs · Vocabulary Builder Congruent Statement Angle Measure Congruent Polygons Congruent Segments Congruent Triangles Proof Algebraic Equation

Unit 2: Congruence, Similarity, and Proofs · Vocabulary Builder Congruent Statement Angle Measure Congruent Polygons Congruent Segments Congruent Triangles Proof Algebraic Equation

Are the following triangles congruent? Why or why not? Write a congruence statement for the triangles.…

Are the following triangles congruent? Why or why not? Write a congruence statement for the triangles.…

cpb-us-e1.wpmucdn.com...CCGPS Geometry Name: 5 - Congruence & Triangles Date: More Practice with Proving Triangles Congruent 5.4 — Classwork Determine whether the triangles are congruent.

cpb-us-e1.wpmucdn.com...CCGPS Geometry Name: 5 - Congruence & Triangles Date: More Practice with Proving Triangles Congruent 5.4 — Classwork Determine whether the triangles are congruent.

Unit 3 Congruence & Proofs Lesson 1: Introduction to ... · • When two right triangles have congruent hypotenuses and a pair of congruent legs, then the triangles are congruent.

Unit 3 Congruence & Proofs Lesson 1: Introduction to ... · • When two right triangles have congruent hypotenuses and a pair of congruent legs, then the triangles are congruent.

4.2 Apply Congruence and Triangles You will identify congruent figures. Essential Question: What are congruent figures? Tell students they will learn how.

4.2 Apply Congruence and Triangles You will identify congruent figures. Essential Question: What are congruent figures? Tell students they will learn how.

Congruent Triangles - Weeblycmwarren.weebly.com/uploads/1/2/0/8/120830366/triangle_congrue… · Congruent Triangles • Congruent triangles have • The parts of congruent triangles

Congruent Triangles - Weeblycmwarren.weebly.com/uploads/1/2/0/8/120830366/triangle_congrue… · Congruent Triangles • Congruent triangles have • The parts of congruent triangles

5 Congruent Chapter Triangles - mRS. HOUKhoukgeometry.weebly.com/uploads/8/3/6/8/8368923/ga_5.1... · 2018. 10. 10. · Naming Congruent TrianglesDetermine whether the congruence

5 Congruent Chapter Triangles - mRS. HOUKhoukgeometry.weebly.com/uploads/8/3/6/8/8368923/ga_5.1... · 2018. 10. 10. · Naming Congruent TrianglesDetermine whether the congruence

Congruent Triangles · Web viewMore Practice with Proving Triangles Congruent Determine whether the triangles are congruent. If they are congruent fill in the congruence statement

Congruent Triangles · Web viewMore Practice with Proving Triangles Congruent Determine whether the triangles are congruent. If they are congruent fill in the congruence statement

7 Triangles CONGRUENCE OF TRIANGLES CONGRUENT ...2. If two sides and an angle of one triangle are equal to two sides and an angle of another triangle, then two triangles must be congruent

7 Triangles CONGRUENCE OF TRIANGLES CONGRUENT ...2. If two sides and an angle of one triangle are equal to two sides and an angle of another triangle, then two triangles must be congruent

Geometry Triangle Congruence Theorems zCongruent triangles have three congruent sides and and three congruent angles. zHowever, triangles can be proved.

Geometry Triangle Congruence Theorems zCongruent triangles have three congruent sides and and three congruent angles. zHowever, triangles can be proved.