1. Warm Up
Simplify the following: 3(-4m + 8) -6(2m – 4) + 10 Solve and graph the solution set for the following inequalities y + 5 ≤ 3 w + 6 < -5
The support of a wood table are in the shape of a right triangle. Find the third angle of the triangle if the measure of one of the angles is 23°. Find the missing measure of the triangle then classify the triangle as acute, right, or obtuse.

2. What is a “unique” triangle?
It is a triangle that has the same shape and size.
Two triangles are considered the same unique triangle if they have the same shape and size, regardless of their positions or orientation.
When you are given 3 side lengths that form a triangle, you will always get a ‘unique’ triangle, because the triangle can only be formed one way with that size and shape.

3. “Infinitely Many Triangles” “One Unique Triangle”
Infinitely many triangles can be drawn when the angle measures of a triangle will produce the same shape (similar), but you can vary the lengths of the sides, making them smaller or larger.
Only one unique triangle can be drawn when the given conditions will not produce any other triangle.

4. Triangle Side Lengths Theorem
To form triangles, the sum of 2 smaller sides must be greater than the longest side.
Will these sides form a triangle?
3 cm, 4 cm, 9 cm
5 cm, 8 cm, 9 cm
2 cm, 3 cm, 5 cm
4 cm, 5 cm, 6 cm NO
YES NO
YES

5. Triangle Angle Sum Theorem
To form triangles, the sum of the interior angles must be 180.° We can form similar triangles, but may not all be the same size. Will these angles form a triangle? 60°, 60°, 60° 60°, 120°, 10° 80°, 70°, 70° 90°, 45°, 45°
YES NO NO
YES

6. Forming Triangles
To form triangles, you must know 3 side lengths, 2 angles and the adjacent side, or 2 sides and an adjacent angle.
Will these combinations of angles and/or sides form a triangle?
80° and 4 cm
100° and 15 cm
80°, 50°, 50°
60°, 30°, 100° NO NO
YES NO

7. Drawing Triangles
Draw a triangle with angles of 80˚, 60˚, and 40˚. What type of triangle have you created?
Draw a triangle with angles of 50˚, 100˚, and 30˚. What type of triangle have you created?