3.5 Overlapping Triangles

Slides:



Advertisements
Similar presentations
4-4 Using Congruent Triangles: CPCTC
Advertisements

Chapter 4.6 Notes: Use Congruent Triangles Goal: You will use congruent triangles to prove that corresponding parts are congruent.
GOAL 1 PLANNING A PROOF EXAMPLE Using Congruent Triangles By definition, we know that corresponding parts of congruent triangles are congruent. So.
I can identify corresponding angles and corresponding sides in triangles and prove that triangles are congruent based on CPCTC.
Day 2 I can understand the concept of congruent figures. I can accurately identify the corresponding parts of figures. Find the number of triangles in.
TODAY IN GEOMETRY…  Review: Finding congruent angles and sides and proving triangles are congruent.  Learning Goal: 4.6 Use CPCTC to prove congruent.
3.5 Overlapping Triangles Objective: After studying this lesson you will be able to use overlapping triangles in proofs.
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.
Lesson 4 – 3 Congruent Triangles
By Shelby Smith and Nellie Diaz. Section 8-1 SSS and SAS  If three sides of one triangle are congruent to three sides of another triangle, then the triangles.
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.
Advanced Geometry 3.3. Objective To write proofs involving congruent triangles and CPCTC.
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.
Bellwork 1)When are two angles congruent? 2)In, if m ∠ A=64° and m ∠ B=71°, what is m ∠ C? 3)What property of angle congruence is illustrated by this statement?
Chapters 2 – 4 Proofs practice. Chapter 2 Proofs Practice Commonly used properties, definitions, and postulates  Transitive property  Substitution property.
Section 3.4 Beyond CPCTC. Median A median of a triangle is a line segment drawn from any vertex of the triangle to the midpoint of the opposite side.
Isosceles and Equilateral Triangles
3.4 Beyond CPCTC Objective:
Section 3.4 Beyond CPCTC.
5.2 Proving Triangles are Congruent by SSS and SAS
Section 4-5 Triangle Congruence AAS, and HL
7.4 Showing Triangles are Similar: SSS and SAS
Using Triangle Congruence to Prove Sides and Angles Congruent C h. 5-2
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
Other Methods of Proving Triangles Congruent
3.2 Three Ways To Prove Triangles Congruent
Proving Triangles Congruent
Proving Triangles Congruent
Vocabulary Corollary Base angles Vertex angles.
Proofs Review.
Warm Up (on the ChromeBook cart)
Proving Triangles Congruent
(4.2) Triangle Congruence by SSS and SAS
Corresponding Parts 4-2D
4-3: Congruent Triangles
Congruent Triangle Proofs
5.5 Proving Triangle Congruence by SSS
More Proving Triangles Congruent
Two-Column Triangle Proofs
Objective! Use CPCTC to prove parts of triangles are congruent.
4.5 ASA and AAS Ways to prove 2 triangles congruent:
5.3 Proving Triangles Congurent using SAS
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.
Proving Triangles Congruent
Warm Up (on handout).
Aim: Do Now: ( ) A B C D E Ans: S.A.S. Postulate Ans: Ans:
AIM: Review of Congruent Triangle Proofs!!!
Section 3.4 Beyond CPCTC.
Geometry Proofs Unit 12 AA1.CC.
Proving Triangles Congruent
4-7 & 10-3 Proofs: Medians Altitudes Angle Bisectors Perpendicular
8.3 Methods of Proving Triangles Similar
Proving Triangles Congruent
4-3: Congruent Triangles
Isosceles/ Equilateral
Congruence in Right Triangles
Proving Triangles Congruent
Triangle Congruence by ASA and AAS
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.
Chapter 5: Quadrilaterals
5-9: Overlapping Triangles and Double Proofs
Advanced Geometry Section 3.7 The Isosceles Triangle Theorem/Converse/Inverse/Contrapositive Learner Objective: Students will solve proofs and problems.
Warm Up 7.4 Is there enough information to prove that the triangles are congruent? If so, state the reason (SSS, SAS, HL, ASA,
4-4/4-5 Proving Triangles Congruent
Chapter 5 Congruent Triangles.
Presentation transcript:

3.5 Overlapping Triangles

Steps: 1. Mark the given information on your diagram and write the givens in your proof. 2. Do anything the givens tell you to do (aka if given bisection, state the now congruent segments or angles). 3. Decide which triangles you will be able to prove congruent. 4. Re-Draw the triangles our corresponding and hopefully use CPCTC to finish the proof.

Mark the given information. P W M T W M P T S W M Mark the given information. Decide which triangles we can prove congruent. Re-Draw the triangles so they are corresponding T M W

Statements Reasons 1. Given 2. Reflexive Prop. 3. SSS 4. CPCTC P W M T

Mark the given information. J H J K G H Mark the given information. Decide which triangles we can prove congruent. Re-Draw the triangles so they are corresponding J H G

Statements Reasons 1. Given F G H J H G Statements Reasons 1. Given If 2 angles are rt. angles, then they are congruent. 3. Reflexive Prop. 4. SAS

Mark the given information. P O T S R P T S T P R Mark the given information. Decide which triangles we can prove congruent. Re-Draw the triangles so they are corresponding P R S T

Statements Reasons N S O T P R 1. Given If a figure is =lateral, then all sides are congruent. 3. Reflexive Prop. 4. SAS 5. CPCTC Subtraction Property If congruent segments are subtracted from congruent segments, then their differences are congruent.

Homework p. 135 # 5 – 11 odd p. 140 # 5, 9 – 12 Study for QUIZ!!!!!