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Scholarship Geometry
Section 4-1: Classifying Triangles
Triangles can be classified by angles or by sides.
Classifying triangles by angles:
Three acute angles
ACUTE
Three congruent angles
EQUIANGULAR
One right angle
RIGHT
One obtuse angle
OBTUSE
Classifying triangles by sides:
Three congruent sides
EQUILATERAL
At least two congruent sides
ISOSCELES
No congruent sides
SCALENE
Ex. 1: Draw an example of each of the following (if possible).
Label congruent sides and right angles.
Acute
Obtuse
Right
NOT POSSIBLE
NOT POSSIBLE
Scalene
Isosceles
Equilateral
Ex. 2: Classify each triangle by its angles.
a) ΔABD
Two angles are 20° and 80°, and since the sum of the angles in a triangle is 180°, then the third
angle is 80° (20 + 80 = 100; 180 – 100 = 80). All of the angles are acute, so the triangle is acute.
b) ΔBDC
∠DBC is 100°, so the triangle is obtuse.
c) ΔADC
∠ADC is a right angle, so the triangle is right.
Ex. 3: Classify each triangle by its sides.
a) ΔHEF
EF = HF = 10, and HE = 12, so it’s isosceles.
b) ΔHEG
HE = 12, HG = 11, and EG = 14, so it’s scalene.
Ex. 4: Find the x and the three side lengths.
Set the two congruent sides equal:
4x – 10.7 = 2x + 6.3
2x = 6.3 + 10.7 = 17
x = 17/2 = 8.5
JK = 4(8.5) – 10.7 = 34 – 10.7 = 23.3
KL = 2(8.5) + 6.3 = 17 + 6.3 = 23.3
JL = 5(8.5) + 2 = 42.5 + 2 = 44.5
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