1. Triangles and Congruence
Chapter 5
Triangles and Congruence

2. Classifying Triangles
Section 5-1
Classifying Triangles

3. Triangle
A figure formed when three noncollinear points are joined by segments

4. Triangles Classified by Angles
Acute Triangle – all acute angles
Obtuse Triangle – one obtuse angle
Right Triangle – one right angle

5. Triangles Classified by Sides
Scalene Triangle – no sides congruent
Isosceles Triangle – at least two sides congruent
Equilateral Triangle – all sides congruent (also called equiangular)

6. Section 5-2
Angles of a Triangle

7. Angle Sum Theorem
The sum of the measures of the angles of a triangle is 180.

8. Theorem 5-2
The acute angles of a right triangle are complementary.

9. Theorem 5-3
The measure of each angle of an equiangular triangle is 60.

10. Section 5-3
Geometry in Motion

11. Translation
When you slide a figure from one position to another without turning it.
Translations are sometimes called slides.

12. Reflection When you flip a figure over a line.
The figures are mirror images of each other.
Reflections are sometimes called flips.

13. Rotation When you turn the figure around a fixed point.
Rotations are sometimes called turns.

14. Pre-image and Image
Each point on the original figure is called a pre- image.
Its matching point on the corresponding figure is called its image.

15. Mapping
Each point on the pre- image can be paired with exactly one point on the image, and each point on the image can be paired with exactly one point on the pre-image.

16. Section 5-4
Congruent Triangles

17. Congruent Triangles
If the corresponding parts of two triangles are congruent, then the two triangles are congruent

18. Corresponding Parts
The parts of the congruent triangles that “match”

19. Congruence Statement Δ ABC ≅ Δ FDE
The order of the vertices indicates the corresponding parts

20. CPCTC
If two triangles are congruent, then the corresponding parts of the two triangles are congruent
CPCTC – corresponding parts of congruent triangles are congruent

21. Section 5-5
SSS and SAS

22. Postulate 5-1
If three sides of one triangle are congruent to three corresponding sides of another triangle, then the triangles are congruent. (SSS)

23. Included Angle
The angle formed by two given sides is called the included angle of the sides

24. Postulate 5-2
If two sides and the included angle of one triangle are congruent to the corresponding sides and included angle of another triangle, then the triangles are congruent. (SAS)

25. Section 5-6
ASA and AAS

26. Postulate 5-3
If two angles and the included side of one triangle are congruent to the corresponding angles and included side of another triangle, then the triangles are congruent.

27. Theorem 5-4
If two angles and a nonincluded side of one triangle are congruent to the corresponding two angles and nonincluded side of another triangle, then the triangles are congruent.