4-1 and 4-2

Classifying Triangles

Angle Relationships in Triangles

Classify Triangles By AnglesType Definition Drawing/Example

Acute

Right

Obtuse

Equiangular

Classify Triangles By SidesType Definition Drawing/Example

Scalene

Isosceles

Equilateral

Classify each triangle by angles and sides

1. ∆ NSE

2. ∆ ANE

3. ∆ AEK

4. ∆ ASK

5. ∆ AES

K

115◦

25◦ 40◦ 70◦E

A

N

S

6

5.1

11810

12

Find the value of x, y and ∆ side lengths

6y

4y + 12

10x – 4

2 – 4x

13 – 2x x2 – 5x – 15

6) 7)

8) You are bending a wire to make a coat hanger. The length of the wire is 65 cm. You need 25 cm to make the hook of the hanger. The triangular portion of the hanger is an isosceles triangle. The length of one leg of this triangle is half the length of the base.

a) Sketch the hanger.

 

b) Give the dimensions of the triangular portion.

Triangle Sum Theorem• The sum of the angles

measures of a triangle is ____________________.

Corollaries of the Thm• Acute angles in a right

triangle are complementary.

• Measure of each angle in an equiangular triangle is 60◦.

Exterior Angle Theorem

The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote (nonadjacent) interior angles.

43

2

1

𝑚<4=𝑚<1+𝑚<2

Third Angles Theorem If two angles of one triangle are congruent to two

angles of another triangle, then the third angles are ____________.

50◦

70◦

70◦

50◦

Ex: Apply the new theorems to solve

(5x + 2) (12x - 4)

64

9) 10) In ∆SMD, m<S=55 and m<M is four times larger than m<D. Find m<M and m<D.