Lesson 4-5 Proving Congruence – ASA, AAS. Ohio Content Standards:

Slides:

Advertisements

Similar presentations

Examining Proofs ©Xtreem Geometry TEKS G.6E.

Advertisements

Chapter 1Foundations for Geometry Chapter 2Geometric Reasoning Chapter 3Parallel and Perpendicular Lines Chapter 4Triangle Congruence Chapter 5Properties.

4.5 Proving Δs are  : ASA and AAS. Objectives: Use the ASA Postulate to prove triangles congruentUse the ASA Postulate to prove triangles congruent Use.

Section 4-3 Triangle Congruence (ASA, AAS) SPI 32C: determine congruence or similarity between triangles SPI 32M: justify triangle congruence given a diagram.

Proving Triangles Congruent At the end of this lesson, you should be able to prove two triangles are congruent by using ASA and AAS Postulates.

GEOMETRY Proving Triangles are Congruent: ASA and AAS.

Topic: Congruent Triangles (6.0) Objectives Prove triangles are congruent Standards Geometry. Measurement. Problem solving. Reasoning and Proof.

Proving Triangles Congruent Advanced Geometry Triangle Congruence Lesson 2.

4.4: Prove Triangles Congruent by ASA and AAS

Chapter 4.5 Notes: Prove Triangles Congruent by ASA and AAS Goal: You will use two more methods to prove congruences.

4.5 – Prove Triangles Congruent by ASA and AAS

4.3 & 4.4 Proving Triangles are Congruent

Congruent Triangles.  Standard 25: Identify interior and exterior angles of a triangle and identify the relationships between them.  Standard 26: Utilize.

Triangle Congruence Postulates T.2.G.1 Apply congruence (SSS …) and similarity (AA …) correspondences and properties of figures to find missing parts of.

SECTION 4.4 MORE WAYS TO PROVE TRIANGLES CONGRUENT.

4-2: Triangle Congruence by SSS and SAS 4-3: Triangle Congruence by ASA and AAS 4-4: Using Corresponding Parts of Congruent Triangles.

Lesson 4-3 Congruent Triangles. Ohio Content Standards:

Lesson 4-1 Classifying Triangles. Ohio Content Standards:

Proving Angle Relationships

Lesson 5-1 Classifying Triangles. Ohio Content Standards:

Today – Wednesday, January 16, 2013  Learning Target: Review Ch.5 by practicing Ch.5 concepts in text book  Review Content from each chapter.

Lesson 6-6 The Pythagorean Theorem. Ohio Content Standards:

Lesson 4-2 Angles of Triangles. Ohio Content Standards:

Postulates and Paragraph Proofs

Lesson 6-5 Parts of Similar Triangles. Ohio Content Standards:

Lesson 2-6 Algebraic Proofs. Ohio Content Standards:

Proving Triangles Congruent. Warm Up Objectives Can you prove triangles congruent using SSS, SAS, ASA, AAS, and HL?

Lesson 2-7 Proving Segment Relationships. Ohio Content Standards:

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 2-4 Deductive Reasoning. Ohio Content Standards.

Lesson 6-3 Similar Triangles. Ohio Content Standards:

Lesson 2-1 Inductive Reasoning and Conjecture. Ohio Content Standards:

1. An Overview of the Geometry Standards for School Mathematics? 2.

Lesson 5-3 GeometryinMotion. Ohio Content Standards:

Geometry 4-5 ASA, AAS, and HL. Vocab. Word An included side is the common side of two consecutive angles in a polygon. (The side in between two angles)

Proving Triangles Congruent

Introduction to Geometric Proof Logical Reasoning and Conditional Statements.

(4.2)/(4.3) Triangle Congruence by SSS, SAS, ASA, or AAS Learning Target: To be able to prove triangle congruency by SSS, SAS, ASA, or AAS using proofs.

Triangle Congruence by ASA and AAS Chapter 4 Section 3.

Triangle Congruence by ASA and AAS Acadamic Geometry.

4.3 Triangle Congruence by ASA and AAS You can prove that two triangles are congruent without having to show that all corresponding parts are congruent.

UNIT 7 LESSON 4B PROVING PARALLELOGRAMS CCSS G-CO 11: Prove theorems about parallelograms. LESSON GOALS Use properties of parallelograms to prove that.

Lesson 5-4 The Triangle Inequality. Ohio Content Standards:

For 9 th /10 th grade Geometry students Use clicker to answer questions.

4-3 Triangle Congruence by ASA and AAS. Angle-Side-Angle (ASA) Postulate If two angles and the included side of one triangle are congruent to two angles.

Lesson 5.3 Proving Triangles are Congruent: ASA and AAS

5.6 Proving Triangle Congruence by ASA and AAS. OBJ: Students will be able to use ASA and AAS Congruence Theorems.

4.4 Proving Triangles are Congruent: ASA and AAS Geometry.

Are the following triangles congruent? Why or why not? Write a congruence statement for the triangles. 21 ° 74 ° 85 ° 21 ° 74 ° 85 ° T S R L M N.

Geometry, Quarter 2, Unit 2.3 Proving Theorems About Parallelograms Days: 11.

ASA AND AAS CONGRUENCE Section 4.5. Angle-Side-Angle (ASA) Congruence Postulate  If two angles and the included side of one triangle are congruent to.

Lesson 4-6 Isosceles Triangles. Ohio Content Standards:

7.5 You Shouldn’t Make Assumptions

Do Now: Identify two congruent triangles in the figure below. H N A D.

Section 4-3 Proving Triangles Congruent by ASA and AAS.

Prove triangles congruent by ASA and AAS

Proving Triangles are Congruent

Continuation of MVP 8.3 PROVE IT!

5.3 Proving Triangles are congruent:

Proofs Geometry - Chapter 2

Lesson 4-4 & 4.5: Proving Δs Congruent

Proving Triangles are Congruent: ASA and AAS

Learn to use the ASA and AAS tests for congruence.

Postulates and Theorems to show Congruence SSS: Side-Side-Side

Triangle Congruence by ASA and AAS

MATH THS – Standard Geometry

Proving Congruence – SSS, SAS

4.3 Triangle Congruence by ASA and AAS

Five-Minute Check (over Lesson 7–3) Mathematical Practices Then/Now

4-4/4-5 Proving Triangles Congruent

Presentation transcript:

Lesson 4-5 Proving Congruence – ASA, AAS

Ohio Content Standards:

Describe and apply the properties of similar and congruent figures; and justify conjectures involving similarity and congruence.

Ohio Content Standards: Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two-dimensional figures and three-dimensional objects.

Ohio Content Standards: Use coordinate geometry to represent and examine the properties of geometric figures.

Ohio Content Standards: Prove or disprove conjectures and solve problems involving two- and three-dimensional objects represented within a coordinate system.

Ohio Content Standards: Analyze two-dimensional figures in a coordinate plane; e.g., use slope and distance formulas to show that a quadrilateral is a parallelogram.

Ohio Content Standards: Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others.

Ohio Content Standards: Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two-dimensional figures and three-dimensional objects.

Ohio Content Standards: Make, test and establish the validity of conjectures about geometric properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof.

Included Side

The side of a triangle that is between two angles.

Postulate 4.3

Angle-Side-Angle Congruence

Postulate 4.3 If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. Angle-Side-Angle Congruence

Write a proof.

R W L E D

Theorem 4.5

Angle-Angle-Side Congruence

Theorem 4.5 If two angles and the nonincluded side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two triangles are congruent. Angle-Angle-Side Congruence

Write a proof.

K J L N M

Assignment: Pgs evens, all