What is a Triangle? Definition of a Triangle: -A plane figure with three straight sides and three angles -It has three edges and three vertices -Triangle Classifications by sides include Scalene, Isosceles, Equilateral –Triangle Classifications by angles include Acute, Right, Obtuse, and Equiangular

Measuring Triangles Area Formula: B= Base H=Height

Quick Quiz How many angles does a triangle have? What is the area formula?

Triangle Classifications By Sides Scalene Triangle-A scalene triangle is a triangle that has three unequal sides Isosceles Triangle-An isosceles triangle is a triangle that has two sides of equal length.Sometimes it is specified as having two and only two sides of equal length Equilateral Triangle-An equilateral triangle is a triangle in which all three of the sides are equal.

Triangle Classifications by Angles There are four ways to classify triangles by their angles Right- 1 right angle Acute- 3 acute angles Obtuse- 1 obtuse angle Equiangular- All angles are equal

Types Of Angles Acute- measures less than 90 degrees but more than 0, Acute triangle has three of these angles. Right- a 90 degree angle, a right triangle only obtains one of these angles. Obtuse- measures more than 90 degrees but less than 180 degrees, Obtuse triangle contains only 1 obtuse angle

Quick Quiz What two ways are triangles classified? Name a triangle that is classified by an angle, then describe it.

Pythagorean theorem ●The pythagorean theorem is one of the earliest theorems known to ancient civilians.This famous theorem is named after the the Greek mathematician and philosopher, Pythagoras. ●The pythagorean theorem is known as a 2 + b 2 = c 2 ●In this photo here is how the Pythagorean theorem is used to find the Hypotenuse of a triangle and the leg of a triangle also using the pythagorean theorem.

Other Triangle Theorems The longest side of a triangle is across from the largest angle The Shortest side of a triangle is across from the shortest angle If two angles are congruent, the sides opposite of those angles are also congruent

Inequality Properties The first inequality property states that the sum of any two sides of a triangle is always greater than third The second inequality property states that when a pair of angles are unequal, so are the sides opposite of them.

Triangle Concepts The inside angles of a triangle all add up to 180° The sum of the lengths of any two sides of a triangle is always greater than the length of the third side. Every two adjacent sides include an angle

Triangle Properties Vertex- The corners of the triangle, each triangle has three vertices. Base- Could be any of the three sides, but usually the side on the bottom. In an Isosceles triangle the base is the unequal side. Area- The number of square units that fill up a triangle. Median- Median of a triangle is a line from a vertex to the midpoint of the opposite side Perimeter- The distance around the outside of the triangle, which is the sum of its sides Interior Angles- the three angles on the inside of the triangle at each vertex Exterior Angles- Angle between a side and a extended adjacent side