Geometry Lesson 4-1 Classifying Triangles

Learning Target You will be able to identify and classify triangles by angles. You will be able to identify and classify triangles by sides.

Measuring Angles Recap How many degrees does a triangle have inside of it? 180

Side and Angle Relationship The side that is opposite of the angle is what is affected by the angle. If it is the biggest angle in a triangle then it will be the biggest side. If it is the smallest angle in a triangle then it will be the smallest side. If two angles are the same then the side lengths will also be the same.

Example: Which side is the longest? Shortest? shortest longest

Classify triangles by angles Acute Triangle: In an acute triangle, all the angle measures are less than 90. A B C ABC is an acute triangle

Classify triangles by angles (cont’d) Right Triangle: In a right triangle, the measure of one of the angles is 90 X YZ XYZ is a right triangle

Classify triangles by angles (cont’d) Obtuse Triangle: In an obtuse triangle, one of the angle measures is more than PQ R PQR is an obtuse triangle

Classify triangles by angles (cont’d) Equiangular Triangle: In an equiangular triangle, all the angle measures are congruent and equal to A CB ABC is an equiangular triangle

Work examples Work Pg. 221 #1, 3, and 6

Classify triangles by sides Scalene Triangle: A triangle in which all three sides have different measures. 10cm 13cm 8cm A B C

Classify triangles by sides (cont’d) Isosceles Triangle: A triangle in which at least two sides are congruent. X Y Z

Classify triangles by sides (cont’d) Equilateral Triangle: A triangle in which all three sides are congruent.

Work examples Work Pg. 221 # 2, 4, and 5 You will have about three minutes After you have completed this draw one of each type of triangle. Again make sure that you are doing this correctly by checking your measurements.

Challenge for sides Think about this question. If you know the answer write it down and raise your hand. HOT: If you are only given the coordinates of the points of the triangle how can you find out how long each side of the triangle is?

Distance Formula If you are given only the coordinates of the triangle use distance formula to find the measures of each side of the triangle. We will work Example 2 on page 218

Challenge for determining if a triangle is a right triangle Think about this question. Write the answer down if you know it. HOT: If you want to know if a triangle is a right triangle or not what can you use? Do you only use it once?

Slope To find out if a triangle is a right triangle you must use slope. You choose two points and find their slope. Then you choose the point left and one of the points that you already used to find its slope. If you multiply the two slopes and they give you -1 (or if they are negative reciprocals) then the triangle is a right triangle.

Interior Angles/Exterior Angles Interior angles are…inside of the triangle – They add up to be…180 degrees Exterior angles are…outside of the triangle. – They form linear pairs with the interior angles.

Solving for variables using all that we know about triangles Example: Find x, QR, RS, and QS if QRS is an equilateral triangle. Solution: 4x = 2x + 1 2x = 1 X = ½ QR = 2, RS = 2, QS = 2. 4x 2x + 1 6x – 1 Q S R

Solving for variables using all that we know about triangles Together we will try Pg. 220 # 3-5

Homework Pg. 221 # 8-36 even; all