© 2012 MARS University of NottinghamAlpha Version January 2012 Projector Resources: Analyzing Congruency Proofs Projector Resources.

Slides:

Advertisements

Similar presentations

4-4 Using Congruent Triangles: CPCTC

Advertisements

4-2 Triangle Congruence by SSS and SAS

6-2: Proving Congruence using congruent parts Unit 6 English Casbarro.

Chapter 4.6 Notes: Use Congruent Triangles Goal: You will use congruent triangles to prove that corresponding parts are congruent.

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

SWBAT: Recognize Congruent Figures and Their Corresponding Parts

Objective: After studying this lesson you will be able to organize the information in, and draw diagrams for, problems presented in words.

Mrs. Rivas 1. three pairs of congruent sides 2. three pairs of congruent angles.

2.11 – SSS, SAS, SSA.

Introduction There are many ways to show that two triangles are similar, just as there are many ways to show that two triangles are congruent. The Angle-Angle.

~adapted from Walch Education PROVING TRIANGLE SIMILARITY USING SAS AND SSS SIMILARITY.

Thursday, January 10, 2013 A B C D H Y P E. Homework Check.

2D Representations of 3D ObjectsProjector Resources 2D Representations of 3D Objects Projector Resources.

Notes Over Congruence When two polygons are ___________their corresponding parts have the _____ _______. congruent same measure 1. Name the corresponding.

Possible Triangle ConstructionsProjector Resources Possible Triangle Constructions Projector Resources.

Congruence in Right Triangles

Section 4.2 Congruence and Triangles. Two figures are congruent if they have exactly the same size and shape.

Congruent Polygons Sec 6.5 GOALS: To identify congruent polygons.

Warm up. 4.3 Analyzing Triangle Congruence Two new shortcuts: AAS HL.

1 Chapter 5 TRIANGLE PROPERTIES Geometry 1 A Practice Problems Pat Brewster.

CHAPTER 4 SECTION 2 Triangle Congruence by SSS and SAS.

4.5 – Prove Triangles Congruent by ASA and AAS In a polygon, the side connecting the vertices of two angles is the included side. Given two angle measures.

Proving Triangles are Congruent: SSS and SAS Sec 4.3

4. 1 Apply Congruence and Triangles 4

5.4 Proving Triangle Congruence by SSS

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.

 When figures have the same size and shape we say they are congruent.  In this lesson I will focus on congruent triangles.

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

Chapter 9, Section 5 Congruence. To be congruent: –corresponding parts (sides/ angles) have the same measure.

Similar Polygons NOTES 8.1 Goals 1)Use Similarity Statements 2)Find corresponding lengths in similar polygons 3)Find perimeters & areas of similar polygons.

Describing and Defining QuadrilateralsProjector Resources Describing and Defining Quadrilaterals Projector Resources.

Evaluating Conditions for CongruencyProjector Resources Evaluating Conditions for Congruency Projector Resources.

By, Mrs. Muller.  If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent

Proving Side-Side-Side. Proving Side-Angle-Side Create a 55 ° angle. Its two sides should be 3.5 and 5 inches long. Enclose your angle to make a triangle.

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

Enlarging Rectangles If you double the length and width of a rectangle

Two Bags of Jellybeans I have two bags A and B. Both contain red and yellow jellybeans. There are more red jellybeans in bag A than in bag B. If I choose.

Evaluating Conditions for Congruency

5.2 Proving Triangles are Congruent by SSS and SAS

5.1 Exploring What Makes Triangles Congruent

5.3 Proving Triangles are congruent:

Describing and Defining Triangles

5.5 Proving Triangle Congruence by SSS

Evaluating Conditions of Congruency

Homework Due Thursday- Comprehensive Test Friday

7-3 Similar Triangles.

Review: Chapter Test 2 CME Geometry.

Similarity, Congruence, & Proofs

Introduction There are many ways to show that two triangles are similar, just as there are many ways to show that two triangles are congruent. The Angle-Angle.

Chapter 4.2 Notes: Apply Congruence and Triangles

Section 20.1: Exploring What Makes Triangles Congruent

4-2 Triangle Congruence by SSS & SAS

Section 20.2: ASA Triangle Congruence

Isosceles/ Equilateral

5.2 ASA Triangle Congruence

Unit 2 – Similarity, Congruence, and Proofs

Warmup Write a congruence statement for the triangles.

Prove Triangles Congruent by SAS

5.3 Congruent Triangles & Proof

Chapter 4 Congruent Triangles.

Evaluating Conditions for Congruency

Possible Triangle Constructions

Introduction There are many ways to show that two triangles are similar, just as there are many ways to show that two triangles are congruent. The Angle-Angle.

Properties of Triangle Congruence

4.5 Proving Triangles are Congruent: ASA and AAS

Chapter 5 Congruent Triangles.

Proving triangles are congruent: sss and sas

Chapter 4: Congruent Triangles 4.2: Proving Triangles Congruent

Presentation transcript:

© 2012 MARS University of NottinghamAlpha Version January 2012 Projector Resources: Analyzing Congruency Proofs Projector Resources

© 2012 MARS University of NottinghamAlpha Version January 2012 Projector Resources: Must the two triangles be congruent? For each card: 1.Draw examples of pairs of triangles A and B that have the properties stated in the card. 2.Decide whether the two triangles must be congruent, and record your decision at the bottom of the card. 3.If you decide that the triangles do not have to be congruent, draw examples and explain why. 4.If you decide that the triangles must be congruent, try to write a convincing proof. 1

© 2012 MARS University of NottinghamAlpha Version January 2012 Projector Resources: Working Together 1Select a card one of you has worked on. Glue it to the middle of a blank sheet. 2Take turns to explain your work to the others. Explain your conclusion, and how you reached that conclusion. Make sure everyone in your group understands your diagrams. 3When everyone who has worked on the same card has had a turn, work together to reach a joint decision for that card. 4On your sheet produce an explanation together that is better than your individual explanations. 5Make sure you discuss Card 8. 2

© 2012 MARS University of NottinghamAlpha Version January 2012 Projector Resources: Look at this statement 3

© 2012 MARS University of NottinghamAlpha Version January 2012 Projector Resources: Jorge’s Proof 4

© 2012 MARS University of NottinghamAlpha Version January 2012 Projector Resources: Kieran’s Proof 5

© 2012 MARS University of NottinghamAlpha Version January 2012 Projector Resources: Cards: Must the two triangles be congruent? 6 1. One side of Triangle A is the same length as one side of Triangle B. 2. Two sides of Triangle A are the same lengths as two sides of Triangle B. 3. Three sides of Triangle A are the same lengths as three sides of Triangle B. 4. One side of Triangle A is the same length as one side of Triangle B and one angle in Triangle A is the same size as one angle in Triangle B. 5. Two sides of Triangle A are the same lengths as two sides of Triangle B and one angle in Triangle A is the same size as one angle in Triangle B. 6. Three sides of Triangle A are the same lengths as three sides of Triangle B. and one angle in Triangle A is the same size as one angle in Triangle B. 7. One side of Triangle A is the same length as one side of Triangle B and two angles in Triangle A are the same sizes as two angles in Triangle B. 8. Two sides of Triangle A are the same lengths as two sides of Triangle B and two angles in Triangle A are the same sizes as two angles in Triangle B. 9. Three sides of Triangle A are the same lengths as three sides of Triangle B. and two angles in Triangle A are the same sizes as two angles in Triangle B.