IGCSE math chapter 24 Congruent_Triangles.pptx

IGCSE math chapter 24 Congruent_Triangles.pptx

1. Chapter 24 Geometrical terms and relationships

2. STARTER: Odd one out a) b) c ) d )

3. Objectives Find out the congruence rule Check two triangles are congruent Congruent Triangles. Keywords: Congruency Triangles

4. Introduction

5. Two shapes are congruent if they are exactly the same size and shape. For example, these triangles are all congruent. Notice that the triangles can be differently oriented (reflected or rotated).

6. SSS Side-Side-Side If all three sets of corresponding sides are congruent, the triangles are congruent ABC MNO A M O N C B

7. SAS Side-Angle-Side If two corresponding sides and the included angles of two triangles are congruent, then the triangles are congruent XYZ FGH X Y Z F G H * The included angle is the angle between the congruent sides

8. ASA Angle-Side-Angle If two sets of corresponding angles and the included sides are congruent, then the triangles are congruent JKL RST J L K T R S * The included side is the side between the two congruent angles

9. AAS Angle-Angle-Side If two sets of corresponding angles and one of the corresponding non-included sides are congruent, then the triangles are congruent EFG TUV E G F T V U

10. HL Hypotenuse-Leg If the hypotenuse and one set of corresponding legs of two right triangles are congruent, then the triangles are congruent CDH RAM A D H R C M

11. Any one of the following four conditions is sufficient for two triangles to be congruent. Condition 1(SSS): ‘All three sides of one triangle are equal to the corresponding sides of the other triangle.’ 2.4cm 2.2cm 3 cm 3 cm 2.4cm 2.2cm This condition is known as SSS (side, side, side).

12. Any one of the following four conditions is sufficient for two triangles to be congruent. Condition 2(SAS): ‘Two sides and the angle between them of one triangle are equal to the corresponding sides and angle of the other triangle.’ This condition is known as SAS (side, angle, side). 4cm 3cm 3cm 4cm 50° 50°

13. Any one of the following four conditions is sufficient for two triangles to be congruent. Condition 3 (ASA): ‘Two angles and the side between of one triangle are equal to the corresponding angles and sides of the other triangle.’ This condition is known as ASA (angle, side, angle). 4cm 4cm 30° 75° 75° 30°

14. Any one of the following four conditions is sufficient for two triangles to be congruent. Condition 4(RHS): ‘Both triangles have a right angle, an equal hypotenuse and another equal side.’ This condition is known as RHS (right angle, hypotenuse, side). 4cm 9 cm 4cm 9 cm

15. Q2. Show that given triangles are congruent  

16. Prove that triangles are congruent

17. Activity 1: Define congruency : Write all rules

18. Activity : 2 Shade congruent shapes with same color

19. Once you have shown that triangle ABC is congruent to triangle PQR by one of the above conditions, it means that: A = P AB = PQ B = Q BC = QR C = R AC = PR In other words, the points ABC correspond exactly to the points PQR in that order. Triangle ABC is congruent to PQR can be written as Δ ABC ≡ Δ PQR. A B C P R Q

20. ACTIVITY

21. ABCD is a kite. Prove that triangle ABC is congruent to triangle ADC. Grade B Grade B 5cm 12cm 12cm 5cm A B C D AB = AD BC = CD AC is common. So: Δ ABC = Δ ADC (SSS)

22. Grade B Grade B The triangles in each pair are congruent. State the condition that shows that the triangles are congruent. 5cm 3 cm 75° 5cm 3 cm 75° 5cm 7cm 4 cm 5cm 7cm 4 cm 7cm 5cm 7cm 5cm 8cm 35° 70° 8cm 35° 70° a) b ) c ) d)

23. Grade A Grade A Draw a rectangle EFGH. Draw in the diagonal EG. Prove that triangle EFG is congruent to triangle EHG. Draw an isosceles triangle ABC where AB = AC. Draw the line from A to X, the midpoint of BC. Prove that triangle ABX is congruent to triangle ACX. In the diagram ABCD and DEFG are squares. Use congruent triangles to prove that AE = CG. Jez says that these two triangles are congruent because of ASA. Explain why he is wrong. 3cm 4 2 ° 35° 3cm 4 2 ° 35°

24. Why did you draw that face?