1. 4.1 Classifying Triangles

2. Objectives Identify and classify triangles by angles
Identify and classify triangles by sides

3. Parts of a Triangle A triangle is a 3-sided polygon
The sides of ∆ABC are AB, BC, and AC
The vertices of ∆ABC are A, B, and C
Two sides sharing a common vertex are adjacent sides
The third side is called the opposite side
All sides can be adjacent or opposite (it just depends which vertex is being used) C A B
adjacent
Side opposite A

4. Classifying Triangles by Angles
One way to classify triangles is by their angles…
Acute all 3 angles are acute (measure < 90°)
Obtuse 1 angle is obtuse (measure > 90°)
Right 1 angle is right (measure = 90°)
An acute ∆ with all angles  is an equiangular ∆ .

5. Example 1:
ARCHITECTURE The triangular truss below is modeled for steel construction. Classify JMN, JKO, and OLN as acute, equiangular, obtuse, or right.

6. Example 1:
Answer:
JMN has one angle with measure greater than 90, so it is an obtuse triangle.
JKO has one angle with measure equal to 90, so it is a right triangle.
OLN is an acute triangle with all angles congruent, so it is an equiangular triangle.

7. Classifying Triangles by Sides
Another way to classify triangles is by their sides…
Equilateral 3 congruent sides
Isosceles 2 or more congruent sides
Scalene no congruent sides

8. Example 2a: Identify the isosceles triangles in the figure if
Isosceles triangles have at least two sides congruent.
Answer: UTX and UVX are isosceles.

9. Example 2b: Identify the scalene triangles in the figure if
Scalene triangles have no congruent sides.
Answer: VYX, ZTX, VZU, YTU, VWX, ZUX, and YXU are scalene.

10. Example 2c: Identify the indicated triangles in the figure.
a. isosceles triangles
Answer: ADE, ABE
b. scalene triangles
Answer: ABC, EBC, DEB, DCE, ADC, ABD

11. Example 3:
ALGEBRA Find d and the measure of each side of equilateral triangle KLM if and
Since KLM is equilateral, each side has the same length. So
5 = d

12. Example 3: Next, substitute to find the length of each side. KL = 7
LM = 7
KM = 7
Answer: For KLM, and the measure of each side is 7.

13. Your Turn:
ALGEBRA Find x and the measure of each side of equilateral triangle if and
Answer:

14. Example 4:
COORDINATE GEOMETRY Find the measures of the sides of RST. Classify the triangle by sides.

15. Example 4: Use the distance formula to find the lengths of each side.
Answer: ; since all 3 sides have different lengths, RST is scalene.

16. Assignment Pre-AP Geometry: Pg. 181 #13 – 18, 22 – 29, 32, 34, 36, 38