Geometry
Name___________________________________
Classifying Triangles by Sides and/or Angles
Date________________ Period____
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Classify each triangle by its sides. Equal sides and equal angles, if any, are indicated in each diagram.
2)
1)
A) scalene
C) isosceles
B) equilateral
B) isosceles
5)
A) equilateral
C) scalene
A) scalene
C) isosceles
B) equilateral
6)
B) isosceles
7)
A) scalene
C) equilateral
B) isosceles
4)
3)
A) scalene
C) equilateral
A) equilateral
C) scalene
A) isosceles
C) scalene
B) equilateral
8)
B) isosceles
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A) isosceles
C) scalene
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B) equilateral
Worksheet by Kuta Software LLC
Classify each triangle by its angles.
10)
9)
A) right
C) acute
B) obtuse
D) equiangular
A) acute
C) equiangular
11)
A) obtuse
C) acute
12)
B) equiangular
D) right
13)
A) acute
C) obtuse
A) acute
C) right
B) obtuse
D) equiangular
14)
B) right
D) equiangular
15)
A) obtuse
C) right
B) right
D) obtuse
A) right
C) obtuse
B) equiangular
D) acute
16)
B) acute
D) equiangular
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A) acute
C) equiangular
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B) right
D) obtuse
Worksheet by Kuta Software LLC
Classify each triangle by its angles and sides. Equal sides and equal angles, if any, are indicated in each
diagram.
18)
17)
A)
B)
C)
D)
right isosceles
obtuse scalene
acute scalene
obtuse isosceles
19)
A)
B)
C)
D)
acute isosceles
acute scalene
equilateral
right isosceles
A)
B)
C)
D)
obtuse scalene
right scalene
acute scalene
acute isosceles
22)
obtuse isosceles
obtuse scalene
right scalene
equilateral
23)
A)
B)
C)
D)
obtuse scalene
equilateral
obtuse isosceles
acute isosceles
20)
21)
A)
B)
C)
D)
A)
B)
C)
D)
A)
B)
C)
D)
equilateral
obtuse scalene
acute isosceles
right isosceles
24)
right scalene
right isosceles
acute scalene
obtuse isosceles
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A)
B)
C)
D)
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right isosceles
obtuse scalene
equilateral
right scalene
Worksheet by Kuta Software LLC
Classify each triangle by its angles and sides.
26)
25)
2.9
7.7
124° 34°
51°
78°
4.4
22°
7.7
9.7
6.5
51°
A)
B)
C)
D)
acute isosceles
obtuse scalene
equilateral
right isosceles
A)
B)
C)
D)
27)
acute isosceles
equilateral
obtuse isosceles
right isosceles
28)
3.7
32°
54°
5.3
32°
4.5
116°
2.2
A)
B)
C)
D)
72°
54°
4.5
A)
B)
C)
D)
acute isosceles
equilateral
acute scalene
obtuse isosceles
29)
22°
right isosceles
acute scalene
obtuse scalene
obtuse isosceles
30)
14.4
2.2
2.4
132°
24°
90°
13.4
A)
B)
C)
D)
2.4
68°
5.4
right isosceles
acute scalene
equilateral
right scalene
31)
24°
4.4
A)
B)
C)
D)
acute scalene
obtuse scalene
obtuse isosceles
right scalene
32)
12.4
8.1
76°
28°
64°
5.5
38° 114°
17.4
4.2
A)
B)
C)
D)
equilateral
acute isosceles
obtuse scalene
acute scalene
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18.7
40°
A)
B)
C)
D)
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acute isosceles
right scalene
acute scalene
obtuse isosceles
Worksheet by Kuta Software LLC
Draw the triangle. Then, find x and the measure of each side of the triangle.
33) Triangle KLM is equilateral with KM = d + 2, LM = 12 − d, and KM = 4d − 13.
34) Triangle ABC is equilateral with AB = 3 x − 2, BC = 2 x + 4, and CA = x + 10.
35) Triangle DEF is isosceles, angle D is the vertex angle, DE = x + 7, DF = 3 x − 1, and EF = 2 x + 5.
36) Triangle FGH is equilateral with FG = x + 5, GH = 3 x − 9, and FH = 2 x − 2.
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Worksheet by Kuta Software LLC
37) Triangle LMN is isosceles, angle L is the vertex angle, LM = 3 x − 2, LN = 2 x + 1, and MN = 5 x − 2.
Find the measures of the sides of triangle RST, sketch the triangle, and classify the triangle by its sides.
38) R(-1,-3), S(4,4), T(8,-1)
39) R(0, 2), S(2, 5), T(4, 2)
40) R(1, 3), S(4, 7), T(5, 4)
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Worksheet by Kuta Software LLC
Answers to Classifying Triangles by Sides and/or Angles
1) A
2) B
3) A
4) B
5) B
6) A
7) A
8) C
9) B
10) C
11) A
12) A
13) B
14) C
15) B
16) B
17) C
18) B
19) D
20) B
21) B
22) D
23) C
24) B
25) B
26) A
27) A
28) D
29) D
30) C
31) C
32) C
33) d=5; each side measures 7
34) x = 6; each side measure = 16
35) x = 4; DE = 11; DF = 11; EF = 13
36) x = 7; HF = 12; GH = 12; FG = 12
37) x = 3; LN = 7; LM = 7; NM = 13
38) RS = 74; ST = 41, RT = 85; RST is scalene because the sides are all different
measures
39) RS = 13; ST = 13; TR = 4; the triangle is isosceles because 2 sides are congruent
40) RS = 5; ST = 10; TR = 17; the triangle is scalene because all sides are different measures
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Worksheet by Kuta Software LLC