geometry lesson 4-1 classifying triangles. learning target you will be able to identify and classify...
TRANSCRIPT
Geometry
Lesson 4-1Classifying 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?
40
55
85
xy
z
shortestlongest
Classify triangles by angles
• Acute Triangle: In an acute triangle, all the angle measures are less than 90.
85
55
40A
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
YZ90
35
55
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 90.
30
130
20P Q
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 60.
60
60
60
A
C B
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
BC
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 + 12x = 1X = ½QR = 2, RS = 2, QS = 2.
4x
2x + 1
6x – 1
Q
SR
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