1. Triangles

2. What have we already learned about triangles?
Congruence:
SSS--If three sides of one triangle are congruent to three sides of  another triangle, then the triangles are congruent.
SAS--If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
ASA--If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
AAS--If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
New
HL--If the hypotenuse and leg of one right triangle are congruent to the corresponding parts of another right triangle, the two right triangles are congruent.
CPCTC--Corresponding parts of congruent triangles are congruent.

3. Things you might already know, but let’s put it all in one place…
The sum of the interior angles of a triangle is 180 degrees
Triangle Inequality Theorem--The sum of the lengths of any two sides of a triangle must be greater than the third side
Longest Side-- In a triangle, the longest side is across from the largest angle. In a triangle, the largest angle is across from the longest side. (Note: The shortest side is across from the smallest angle, too.)
Mid-segment Theorem--The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long.

4. Classifying Triangles
By side lengths
Scalene—all three sides are different lengths
All angles are different
Isosceles—two sides are the same length
Base angles are congruent
Equilateral—all sides are the same length
All angles are congruent
By angles
Acute—all angles are acute (less than 90°)
Right—one right angle
The side opposite the right angle is called the hypotenuse
The other two sides are called the legs
Pythagorean Theorem—
Obtuse—one angle is obtuse (greater than 90°)

5. Problems…
70°
60 ° x

6. Problems

7. Problems