Using Triangle Congruence to Prove Sides and Angles Congruent C h. 5-2

Slides:

Advertisements

Similar presentations

How do we prove triangles congruent using Side-Side-Side Postulate?

Advertisements

4-4 Using Congruent Triangles: CPCTC

1Geometry Lesson: Congruent Polygons, Triangles, SAS Aim: What are congruent polygons? How do we prove triangles congruent using Side-Angle-Side Postulate?

4-4 & 4-5: Tests for Congruent Triangles

Proving Triangles Congruent Advanced Geometry Triangle Congruence Lesson 2.

Corresponding Parts of Congruent Triangles Lesson 4-4.

Congruent Triangles – Pairs of Triangles Page 11.

TODAY IN GEOMETRY…  Review: Finding congruent angles and sides and proving triangles are congruent.  Learning Goal: 4.6 Use CPCTC to prove congruent.

1Geometry Lesson: Isosceles and Equilateral Triangle Theorems Aim: What theorems apply to isosceles and equilateral triangles? Do Now: C A K B Given: Prove:

ADVANCED GEOMETRY 3.1/2 What are Congruent Figures? / Three ways to prove Triangles Congruent. Learner Objective: I will identify the corresponding congruent.

TODAY IN GEOMETRY…  Go over proofs from HW #5  4.4 WS Warm Up  Learning Goal: 4.5 You will use postulates Angle-Side-Angle and Angle-Angle-Side to prove.

Lesson 2.6 p. 109 Proving Statements about Angles Goal: to begin two-column proofs about congruent angles.

Geometry St. Barnabas H.S. Bronx, NY Geometry Lesson: First Postulates1.

How do we prove triangles congruent using Side-Side-Side Postulate?

Unit 2 Part 4 Proving Triangles Congruent. Angle – Side – Angle Postulate If two angles and the included side of a triangle are congruent to two angles.

1Geometry Lesson: Pairs of Triangles in Proofs Aim: How do we use two pairs of congruent triangles in proofs? Do Now: A D R L B P K M.

Proving Congruence – SSS, SAS Side-Side-Side Congruence Postulate (SSS) If the sides of one triangle are congruent to the sides of a second triangle, then.

4.4 Isosceles Triangles, Corollaries, & CPCTC. ♥Has at least 2 congruent sides. ♥The angles opposite the congruent sides are congruent ♥Converse is also.

Δ CAT is congruent to Δ DOG. Write the three congruence statements for their SIDES

TODAY IN GEOMETRY…  REVIEW: SSS, SAS, HL, ASA, AAS  WARM UP: PROOF-A-RAMA 1  Learning Goal: 4.6 Use CPCTC to prove congruent parts of a triangle  Independent.

Using Special Quadrilaterals

4-4 Using Corresponding Parts of Congruent Triangles I can determine whether corresponding parts of triangles are congruent. I can write a two column proof.

Triangle Proofs. USING SSS, SAS, AAS, HL, & ASA TO PROVE TRIANGLES ARE CONGRUENT STEPS YOU SHOULD FOLLOW IN PROOFS: 1. Using the information given, ______________.

Honors Geometry Section 4.3 cont. Using CPCTC. In order to use one of the 5 congruence postulates / theorems ( )we need to show that 3 parts of one triangle.

Isosceles Triangles, Corollaries, & CPCTC

Prove triangles congruent by ASA and AAS

Geometry-Part 7.

Proving Triangles are Congruent

Sections 6.3 & 6.4 Proving triangles are similar using AA, SSS, SAS

Aim: How do we prove triangles congruent using the Angle-Angle-Side Theorem? Do Now: In each case, which postulate can be used to prove the triangles congruent?

Proving Triangles Congruent: SSS and SAS

4-2 Triangle Congruence by SSS and SAS

Isosceles and Equilateral Triangles Ch. 5-3

Warm Up (on the ChromeBook cart)

Proving Triangles Congruent

Three ways to prove triangles congruent.

(4.2) Triangle Congruence by SSS and SAS

4-2 Triangle Congruence by SSS and SAS

Line Segments Associated with Triangles Ch. 5-1

Corresponding Parts 4-2D

Warm-Up Determine if the following triangles are congruent and name the postulate/definitions/properties/theorems that would be used to prove them congruent.

Two-Column Triangle Proofs

Ways to Prove Triangles Congruent

4.4 Proving Triangles are Congruent by ASA and AAS

4-2 Some Ways to Prove Triangles Congruent (p. 122)

K Aim: Do Now: How do we prove overlapping triangles are congruent? State the names of two triangles in each diagram: 2) F M B R H 1) A B C D 3)

Objective: To use and apply properties of isosceles triangles.

ABC DEF? Is Do Now: When two triangles are congruent:

Proving Triangles Congruent

Warm Up (on handout).

Aim: Do Now: ( ) A B C D E Ans: S.A.S. Postulate Ans: Ans:

Class Greeting.

4-7 & 10-3 Proofs: Medians Altitudes Angle Bisectors Perpendicular

8.3 Methods of Proving Triangles Similar

Proving Triangles Congruent

Lesson Similarity of Triangles

Warmup Write a congruence statement for the triangles.

Proving Triangles Congruent

What theorems apply to isosceles and equilateral triangles?

Ex: Given: Prove: CPCTC:

Proving Triangles Congruent

Triangle Congruence Obj: learn all the ways to prove triangles are congruent To Identify- SSS, AAS, SAS, or ASA.

CPCTC and Circles Advanced Geometry 3.3.

Warm Up 7.4 Is there enough information to prove that the triangles are congruent? If so, state the reason (SSS, SAS, HL, ASA,

Warm Up 1 ( Write a congruence statement

4-4/4-5 Proving Triangles Congruent

Warm Up March 18 Find x Find x R 23 x 2x-1° 4x° 2 13 x° S T.

4-2 Triangle congruence by sss & sas

Proving triangles are congruent: sss and sas

Presentation transcript:

Using Triangle Congruence to Prove Sides and Angles Congruent C h. 5-2 Geometry St. Barnabas HS Bronx, NY Geometry Lesson: Proving Segments and Angles of Triangles Congruent

How do we prove corresponding segments and angles of triangles congruent? Aim: Do Now: ( ) A B C D E Ans: S.A.S. Postulate Ans: Ans:

CPCTC: Corresponding Parts of Congruent Triangles are Congruent. From the definition of congruent triangles: A B C D Ex: Given: Prove: Statements Reasons 1) 2) 3) 4) 5) 6) 7) Given Given Def. angle bisector Reflexive Postulate A.S.A. Postulate C.P.C.T.C. C.P.C.T.C.

T L N X Z R V Q Proofs w/CPCTC 1) Given: Prove: 2) Given: Prove: 1 3 2 4 Q T S N D F 3) Given: Prove:

N R T D D Z B R E Q S N T B 4) Given: Prove: 5) Given: Prove: Proofs w/CPCTC 4) Given: Prove: 5) Given: Prove: D Z B R E Q S N T B 6) Given: Prove: Geometry Lesson: Proving Segments and Angles of Triangles Congruent

1 3 2 4 Q T S N D F 3) Given: Prove: Given Def. Perpendicular Given Solution #3 Statements Reasons 1) 2) 3) 4) 5) 6) 7) 8) Given Def. Perpendicular Given Def. line bisector S.A.S. Postulate C.P.C.T.C Geometry Lesson: Proving Segments and Angles of Triangles Congruent

N R T D 4) Given: Prove: Given Reflexive postulate S.S.S. postulate Solution #4 Statements Reasons 1) 2) 3) 4) 5) Given Reflexive postulate S.S.S. postulate C.P.C.T.C. Def. angle bisector