How do we analyze the relationships between sides and angles in triangles? AGENDA: Warmup Triangle Notes/Practice

Warmup: Angle 1 = 38°, angle 3 = 4x – 8, and angle 5 = 3x Solve for x. **There are multiple ways to solve this!! Talk to the people around you and see if you can come up with the answer and 2 different ways to get it!!**

A C B We name triangles by three vertices. Example: ∆ ABC The sides of a triangle are segments. Examples: AB, BC, AC

Classifying Triangles -- By sides Scalene Triangle – a triangle with no congruent sides. Isosceles Triangle – a triangle with at least 2 congruent sides. Equilateral Triangle – a triangle with three congruent sides.

Triangle Inequality Rule: The sum of the lengths of the two shortest sides of a triangle must be greater than the length of the third side > 6 2, 3, < , 4, 6

Classifying Triangles -- By angles Acute Triangle – all three angles measure less than 90. Obtuse Triangle – one angle measures between 90 and 180. Equiangular Triangle – all three angles are congruent Right Triangle – one angle that measures 90

Examine the following triangles – do you notice any relationship between the angles and sides of the triangles? 80° 20° 5 in 3 in 100° 60° 20° 10 in 5 in 7 in Example 2 Example 3 Example 1 4 in 60°

In triangles, each angle and its corresponding opposite side are related. In each triangle the largest angle is across from the longest side; the smallest angle is across from the shortest side. 7 in 5 in 3 in A B C  B is the largest angle  C is the smallest angle m  A is in between m  B and m  C Example 3

5 in 7 in X Y Z  Y is the largest angle  X and  Z are the same measure. They are both less than m  Y. J KL  J,  K, and  L are all the same measure. 7 in Example 4 Example 5 This triangle is Equilateral and Equiangular.

70° 90° 20° F D E J H G DE is the longest side DF is the shortest side The length of FE is in between the lengths of the other two sides. 50° 80° JH is the longest side GJ and GH have the same length. The length is less than the length of JH. Example 6 Example 7

The congruent sides are called the legs of the triangle. The third side is called the base. The two angles across from the legs are called the base angles. The angle across from the base is called the vertex angle. ***If 2 sides of a triangle are congruent, then the angles opposite them are congruent and vice versa. Base Angles Base Leg Vertex Angle MORE ABOUT ISOSCELES TRIANGLES *The base of a triangle does not have to be on the bottom

Example 52 ° 5x + 7 What kind of triangle is this? Solve for x What is the measure of the remaining angle?

EXAMPLE 2 5x – 10 3x 15 WHAT KIND OF TRIANGLE IS THIS? SOLVE FOR X

EXAMPLE 3 WHAT KIND OF TRIANGLE IS THIS? SOLVE FOR X 13 X + 8