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