1. © 2012 MARS University of NottinghamAlpha Version January 2012 Projector Resources: Analyzing Congruency Proofs Projector Resources

2. © 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

3. © 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

4. © 2012 MARS University of NottinghamAlpha Version January 2012 Projector Resources: Look at this statement 3

5. © 2012 MARS University of NottinghamAlpha Version January 2012 Projector Resources: Jorge’s Proof 4

6. © 2012 MARS University of NottinghamAlpha Version January 2012 Projector Resources: Kieran’s Proof 5

7. © 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.