1. ~ ≅ SIMILAR TRIANGLES SIMILAR SAME SHAPE, BUT NOT SAME SIZE CONGRUENT
SAME SHAPE, SAME SIZE ≅
SIGN FOR CONGRUENT
SIMILAR
SAME SHAPE,
BUT NOT SAME SIZE ~
SIGN FOR SIMILAR

2. AA SSS (similarity) SAS (similarity)
5 WAYS TO PROVE TRIANGLES CONGRUENT SSS SAS ASA AAS HL
3 WAYS TO PROVE TRIANGLES SIMILAR AA
SSS (similarity)
SAS (similarity)

3. ANGLE-ANGLE (AA) SIMILARITY POSTULATE
If two angles of one triangle are congruent to two angles of another triangle, then two triangles are similar.

4. Which triangles are similar to ΔEFG? Explain?
EXAMPLE
Which triangles are similar to ΔEFG? Explain? E 60 F G A. B. C. 70 60 35

5. Which triangles are similar to ΔEFG? Explain?
EXAMPLE
Which triangles are similar to ΔEFG? Explain? E 70 G F A. B. C. 70 40 45

6. EXAMPLE
Is ABC ~ DBE? Explain why? B 50 D E 50 A C

7. SIDE-SIDE-SIDE (SSS) SIMILARITY POSTULATE
If the corresponding side lengths of two triangles are proportional, then the triangles are similar.
If 𝐴𝐵 𝑅𝑆 = 𝐵𝐶 𝑆𝑇 = 𝐶𝐴 𝑇𝑅 , then ΔABC ~ ΔRST A R T S C B

8. Is ΔDEF or ΔGHJ similar to ΔABC?
EXAMPLE
Is ΔDEF or ΔGHJ similar to ΔABC? B 12 8 A C 16 12 G D F 5 4 6 9 J H E 8

9. Is ΔDEF or ΔGHJ similar to ΔABC?12 D F G 12 8 6 5 4 9 E J H 16 8
Shortest Side Longest Side Remaining Side 𝐴𝐵 𝐷𝐸 = 8 6 = 4 3 𝐶𝐴 𝐹𝐷 = = 4 3 𝐵𝐶 𝐸𝐹 = 12 9 = 4 3 𝐵𝐶 𝐺𝐻 = 8 4 = 2 1 𝐶𝐴 𝐽𝐻 = 16 8 = 2 1 𝐵𝐶 𝐽𝐺 = 12 5 = 12 5

10. SIDE-ANGLE-SIDE (SAS) SIMILARITY POSTULATE
If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar.
If <A ≅ <R 𝐴𝐵 𝑅𝑆 = 𝐶𝐴 𝑇𝑅 , then ΔABC ~ ΔRST A R T S C B

11. Is ΔABC similar to ΔEFG? Explain?
EXAMPLE
Is ΔABC similar to ΔEFG? Explain? E 24 F G 28 A 18 C B 21