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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.