Geometry Lesson 4 1 Classifying Triangles Learning Target

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? longest shortest

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

Classify triangles by angles (cont’d) • Right Triangle: In a right triangle, the measure of one of the angles is 90 X 35 90 Z XYZ is a right triangle 55 Y

Classify triangles by angles (cont’d) • Obtuse Triangle: In an obtuse triangle, one of the angle measures is more than 90. R 130 20 P PQR is an obtuse triangle 30 Q

Classify triangles by angles (cont’d) • Equiangular Triangle: In an equiangular triangle, all the angle measures are congruent and equal to 60. A 60 60 C 60 ABC is an equiangular triangle B

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. A 13 8 cm cm C 10 cm B

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 Q equilateral triangle. 6 x – 1 4 x • Solution: 4 x = 2 x + 1 2 x = 1 X=½ QR = 2, RS = 2, QS = 2. R QRS is an 2 x + 1 S

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

Homework • Pg. 221 # 8 -36 even; 44 -47 all