2. Triangle Basics

3. Parts of a Triangle Sides A B C Segment AB, AC, BC Points A, B, C Angles A, B, C Angles Vertices

4. Classification by Angles Acute Obtuse Right Equiangular

5. Classification by Sides Scalene Isosceles Equilateral

6. Interior angles of a Triangle The interior angles of a triangle always add up to 180°!

7. Congruent Triangles Exercise 8.10

8. What does Congruent Mean? Two objects are congruent if they have the same dimensions and shape. Very loosely, you can think of it as meaning ‘EQUAL’. Two LINES are congruent if they have the same length. Two ANGLES are congruent if they have the same value.

9. Congruent Triangles Congruent Shapes have an equal number of sides, and all the corresponding sides and angles are congruent. However, they can be in a different location, rotated or flipped over. So for example the two triangles shown on the right are congruent even though one is a mirror image of the other

10. Conditions for Congruency of Triangles Two sides and the included angle equal. (SAS) Two angles and a corresponding side equal. (AAS) Right angle, hypotenuse and side (RHS) Three sides equal. (SSS)

11. Which congruency do these triangles represent: SIDE –SIDE – SIDE (SSS) SIDE –ANGLE – SIDE (SAS) ANGLE–ANGLE – SIDE (AAS) RIGHT–HYPOTENUSE– SIDE (RHS) SAS, AAS, SSS or RHS?

12. 35 o 120 o 8 cm 10 cm 4 cm 8 cm 10 cm 8 cm 120 o 4 cm 25 o 35 o 120 o 25 o 4 cm 35 o 120 o 10 cm 8 cm 4 cm 10 cm 120 o 8 cm 35 o Not to Scale! 1 2 3 4 5 6 Decide which of the triangles are congruent to the red triangle, giving reasons. SSS SAS AAS RH S    SAS  SSS  AAS  SAS

13. 5 cm 12 cm 13 cm 20 o 13 cm 20 o 70 o 13 cm 12 cm 13 cm 12 cm 5 cm 13 cm 5 cm 13 cm 70 o 13 cm 70 o 20 o Decide which of the triangles are congruent to the yellow triangle, giving reasons. SSS SAS AAS RH S 1 2 3 4 5 6 Not to Scale!  RH S  SSS   RH S  AAS  SAS

14. Similar Triangles Exercise 8.11

15. Similar Triangles Two Triangles that have two angles that are the same in size are know as SIMILAR Similar triangles may be different in size but corresponding side lengths can always be calculated as the same ratio Corresponding Ratios 90 ÷ 45 = 2 80 ÷ 40 = 2 100 ÷ 50 = 2

16. What is the ratio between each of these congruent triangle pairs 1.Find the similar side - 4cm and 8 cm 2.Find the ratio 8cm ÷ 4cm = 2 3. Find the similar side for x 2cm side 4. Use the ratio to calculate X 2cm x 2 (Ratio) = X X = 4cm 1.Find the similar side - 6cm and 18 cm 2.Find the ratio 18cm ÷ 6cm = 3 3. Find the similar side for x 6cm side 4. Use the ratio to calculate X 6cm ÷ 3 (Ratio) = X X = 2cm

17. Harder Examples: 1.5cm+ 2.5cm = 4cm 1.Find the two similar triangles: i.Triangle ABC ii.Triangle ADE A B C D E 2. Find the similar sides i.4cm and the 1.5cm ii.X and 1.2cm 3. Calculate the Ratio: i.4cm ÷ 1.5cm = 2.6 4. Calculate the X value: i.1.2cm x 2.6 (ratio) = 3.2cm

18. Lets try this example