1. In your math notebook show which sides are congruent to prove the triangles are congruent:F

2. Prove Triangles Congruent by SAS and HL

3. Prove Triangles Congruent by SAS and HL
Draw two lines of any length on a paper.

4. Prove Triangles Congruent by SAS and HL
Draw two lines of any length on a paper.
Fold the paper in half along the ends of your lines.

5. Prove Triangles Congruent by SAS and HL
Draw two lines of any length on a paper.
Fold the paper in half along the ends of your lines.
Draw a line along your fold.

6. Prove Triangles Congruent by SAS and HL
Draw two lines of any length on a paper.
Fold the paper in half along the ends of your lines.
Draw a line along your fold.
Are the two triangles congruent?

7. Prove Triangles Congruent by SAS and HL
Draw two lines of any length on a paper.
Fold the paper in half along the ends of your lines.
Draw a line along your fold.
Are the two triangles congruent?
The triangles are congruent because they have two congruent sides with a congruent angle in the middle.

8. Prove Triangles Congruent by SAS and HL
Side-Angle-Side (SAS) Postulate:

9. Prove Triangles Congruent by SAS and HL
Side-Angle-Side (SAS) Postulate:
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.

10. Prove Triangles Congruent by SAS and HL
Side-Angle-Side (SAS) Postulate:
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.
In other words:

11. Prove Triangles Congruent by SAS and HL
Side-Angle-Side (SAS) Postulate:
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.
In other words:
If the two sides containing the same angle are the same, the triangles are the same.

12. Prove Triangles Congruent by SAS and HL
Side-Angle-Side (SAS) Postulate:
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.
In other words:
If the two sides containing the same angle are the same, the triangles are the same.

13. Prove Triangles Congruent by SAS and HL
AB = DE B E A C D F

14. Prove Triangles Congruent by SAS and HL
AB = DE
BC = EF B E A C D F

15. Prove Triangles Congruent by SAS and HL
AB = DE
BC = EF
BAC = EDF B E A C D F

16. Apply what you know:
Parallel sides:

17. Does the angle have to be between the two congruent sides?

18. Right triangles:

19. Right triangles:
The sides next to the right angle are called “legs”.

20. Right triangles: The sides next to the right angle are called “legs”.
The side across from the right angle is called the “hypotenuse”.

21. Right triangles: The sides next to the right angle are called “legs”.
The side across from the right angle is called the “hypotenuse”.
Hypotenuse-Leg (HL) Congruence Theorem:

22. Right triangles: The sides next to the right angle are called “legs”.
The side across from the right angle is called the “hypotenuse”.
Hypotenuse-Leg (HL) Congruence Theorem:
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent.

23. Right triangles: The sides next to the right angle are called “legs”.
The side across from the right angle is called the “hypotenuse”.
Hypotenuse-Leg (HL) Congruence Theorem:
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent.
In other words:

24. Right triangles: The sides next to the right angle are called “legs”.
The side across from the right angle is called the “hypotenuse”.
Hypotenuse-Leg (HL) Congruence Theorem:
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent.
In other words:
If a leg and hypotenuse are the same, the triangles are the same.

25. Right Triangles

26. Right Triangles
Are these triangles congruent?

27. Are the roofs of the houses congruent? How do you know?
Angles

28. Are the roofs of the houses congruent? How do you know?B A
Put in the angle.

29. Are the triangles congruent? How do you know?
Put in the hypotenuse and leg.

30. Brandon Roy shoots a shot from the X, and also from the Y
Brandon Roy shoots a shot from the X, and also from the Y. How far away does the Y have to be to make the triangles congruent?
Draw two triangles showing different placements on the floor.

31. Do you travel the same distance going up each flight of stairs
Do you travel the same distance going up each flight of stairs? How do you know?
Put in height of the left of 10 feet and length on the right of 10 Length on the left of 7 and height on the right of 7 feet. Draw a straight up and down line and side to side to show.

32. Assignment:
Pages
Numbers 3-15 Even, All