Warm UpSimplify 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.

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.

“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.

Triangle Side Lengths TheoremTo 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

NO

YES

YES

Triangle Angle Sum TheoremTo 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

YES

NO

NO

Forming TrianglesTo 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

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?