Ways to prove triangles congruent:

Slides:

Advertisements

Similar presentations

Warm Up Lesson Presentation Lesson Quiz.

Advertisements

Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC

Proving Triangles Congruent

Blue – 3/9/2015 Gold – 3/10/2015.  Last 2 classes, we talked about 3 ways we can determine triangle congruence.  CPCTC – All 3 sides and 3 angles of.

4-7 Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC

Warm Up 1. If ∆ABC  ∆DEF, then A  ? and BC  ?. 2. What is the distance between (3, 4) and (–1, 5)? 3. If 1  2, why is a||b? 4. List methods used.

4-6 Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC

11. No, need  MKJ   MKL 12. Yes, by Alt Int Angles  SRT   UTR and  STR   URT; RT  RT (reflex) so ΔRST  ΔTUR by ASA 13.  A   D Given  C 

Section 7 : Triangle Congruence: CPCTC

Holt Geometry 4-6 Triangle Congruence: CPCTC Warm Up 1. If ∆ABC  ∆DEF, then A  ? and BC  ?. 2. What is the distance between (3, 4) and (–1, 5)? 3.

4-6 Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC

4-6 Triangle Congruence: CPCTC Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal Geometry.

4-6 Triangle Congruence: CPCTC Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

Holt Geometry 4-6 Triangle Congruence: CPCTC 4-6 Triangle Congruence: CPCTC Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson.

Warm Up 1. If ∆ABC  ∆DEF, then A  ? and BC  ?. 2. What is the distance between (3, 4) and (–1, 5)? 3. If 1  2, why is a||b? 4. List methods used.

4-6 Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC

________________ is an abbreviation for the phrase “Corresponding Parts of Congruent Triangles are Congruent.” It can be used as a justification in a proof.

Warmup: One of the sides of an isosceles triangle is 6 cm. If another side is 12 cm, what is the greatest possible perimeter the triangle could have?

4-6 Triangle Congruence: CPCTC Holt Geometry.

Warm Up 1. If ∆ABC  ∆DEF, then A  ? and BC  ? .

Geometry 4-6 CPCTC. Definition  Corresponding Parts of Congruent Triangles are Congruent (CPCTC)  If two triangles are congruent, then all of their.

4-7 Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC

Geometry-Part 7.

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

4-8 Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC

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

Proving Triangles Congruent

Objective! Use CPCTC to prove parts of triangles are congruent.

Proving Triangles Congruent

Proving Triangles Congruent

Warm Up (on the ChromeBook cart)

Three ways to prove triangles congruent.

Proving Parts of Triangles using CPCTC

4-7 Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC

4-6 Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC

Objective! Use CPCTC to prove parts of triangles are congruent.

4-7 Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC

4-7 Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC

Proving Triangles Congruent

4.5 ASA and AAS Ways to prove 2 triangles congruent:

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

5.7 Vocabulary CPCTC CPCTC is an abbreviation for the phrase “Corresponding Parts of Congruent Triangles are Congruent.” It can be used as a justification.

4-6 Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC

Objective Use CPCTC to prove parts of triangles are congruent.

Lessons 4-4 and 4-5 Proving Triangles Congruent.

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

4-6 Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC

Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC

Proving Triangles Congruent

Warm-Up Which congruence shortcut, if any,

~ ≅ SIMILAR TRIANGLES SIMILAR SAME SHAPE, BUT NOT SAME SIZE CONGRUENT

CPCTC uses congruent triangles to prove corresponding parts congruent.

Essential Question: What do I need to know about two triangles before I can say they are congruent?

8.3 Methods of Proving Triangles Similar

4-7 Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC

Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC 4-4

Proving Triangles Congruent

Proving Triangles Congruent

Isosceles/ Equilateral

Unit 2 – Similarity, Congruence, and Proofs

Objective We will analyze congruent triangles

Similar Similar means that the corresponding sides are in proportion and the corresponding angles are congruent. (same shape, different size)

Proving Triangles Congruent

4-6 Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC

4-6 Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC

Lesson 8.04 Triangle Congruence

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

Proving Triangles Congruent

Basic Geometry Section 4-6: Triangle Congruence: CPCTC

Presentation transcript:

Ways to prove triangles congruent: By definition (all 6 parts) By rigidity (SSS, SAS, ASA, AAS, HL)

What is true once triangles are congruent? The Corresponding parts of the congruent triangles are congruent! “CPCTC” The triangles MUST be congruent FIRST

Example 1 Given: YW bisects XZ, XY  YZ. Prove: XYW  ZYW Z

Example 3: Using CPCTC in a Proof Prove: MN || OP Given: NO || MP, N  P

Example 4: Using CPCTC In the Coordinate Plane Given: D(–5, –5), E(–3, –1), F(–2, –3), G(–2, 1), H(0, 5), and I(1, 3) Prove: DEF  GHI Step 1 Plot the points on a coordinate plane.

Step 2 Use the Distance Formula to find the lengths of the sides of each triangle.

So DE  GH, EF  HI, and DF  GI. Therefore ∆DEF  ∆GHI by SSS, and DEF  GHI by CPCTC.