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Geometry Tutor
Worksheet 5
Types of Triangles
2 © MathTutorDVD.com
Geometry Tutor - Worksheet 5 – Types of Triangles
1. Triangles are classified by the lengths of their ______ and measures of their
______.
2. A triangle with three congruent sides or three congruent angles is called an
______ triangle.
3. A triangle with all three angles having a different measure or all three sides
having a different length is called a ______ triangle.
4. A triangle with exactly two sides with the same length is called an ______
triangle.
5. A triangle with one angle having a measure that is greater than 90° is called an
______ triangle.
6. A triangle with one angle having a measure of exactly 90° is called a ______
triangle.
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7. Classify ∆𝐴𝐵𝐶 using its sides and angles.
8. Classify ∆𝐷𝐸𝐹 using its sides and angles.
9. Classify ∆𝐺𝐻𝐽 using its sides and angles.
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10. Classify ∆𝐴𝐵𝐶 using its sides and angles.
11. Classify ∆𝐴𝐵𝐶 using its sides and angles.
12. Classify ∆𝐹𝐸𝐺 using its sides and angles.
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13. Classify ∆𝑋𝑌𝑍 using its sides and angles.
14. Classify ∆𝑈𝑉𝑊 using its sides and angles.
15. Classify ∆𝐷𝐸𝐹 using its sides and angles.
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16. Classify ∆𝑅𝑆𝑇 using its sides and angles.
17. Classify ∆𝐷𝐸𝐹 using its sides and angles.
18. Classify ∆𝐻𝐽𝐾 using its sides and angles.
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19. Solve for 𝑥 in the figure below.
20. Solve for 𝑓 in the figure below.
21. Solve for 𝑥 in the figure below.
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22. Solve for 𝑧 in the figure below.
23. Solve for 𝑥 in the figure below.
24. Solve for 𝑥 in the figure below.
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25. Solve for 𝑥 in the figure below.
26. Suppose the measures of a triangle are labeled 𝑥°, 2𝑥°. and 3𝑥°. What are the
measures of the three angles of the triangle?
27. Solve for 𝑥 in the figure below.
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28. Solve for 𝑥 in the figure below.
29. Solve for 𝑥 in the figure below.
30. Solve for 𝑥 in the figure below.
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Answers - Geometry Tutor - Worksheet 5 – Types of Triangles
1. Triangles are classified by the lengths of their ______ and measures of their
______.
Answer: sides, angles
2. A triangle with three congruent sides or three congruent angles is called an
______ triangle.
Answer: equilateral
3. A triangle with all three angles having a different measure or all three sides
having a different length is called a ______ triangle.
Answer: scalene
4. A triangle with exactly two sides with the same length and exactly two angles
with the same measure is called an ______ triangle.
Answer: isosceles
5. A triangle with one angle having a measure that is greater than 90° is called an
______ triangle.
Answer: obtuse
6. A triangle with one angle having a measure of exactly 90° is called a ______
triangle.
Answer: right
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7. Classify ∆𝐴𝐵𝐶 using its sides and angles.
The triangle has a 90° angle which is a right angle. The other angles both have
different measures.
Answer: right scalene triangle
8. Classify ∆𝐷𝐸𝐹 using its sides and angles.
The angles all have measures of less than 90° which are acute angles. The lengths
of two sides are exactly the same.
Answer: acute isosceles triangle
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9. Classify ∆𝐺𝐻𝐽 using its sides and angles.
The angles all have different acute measures, which means the sides all have
different lengths.
Answer: acute scalene triangle
10. Classify ∆𝐴𝐵𝐶 using its sides and angles.
The triangle has a right angle and two congruent angles.
Answer: right isosceles triangle
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11. Classify ∆𝐴𝐵𝐶 using its sides and angles.
The triangle has an obtuse angle and two other angles with the same measure,
which means two of the sides have the same length.
Answer: obtuse isosceles triangle
12. Classify ∆𝐹𝐸𝐺 using its sides and angles.
The figure shows that the angles all have the same measure and the sides all have
the same length.
Answer: equilateral triangle
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13. Classify ∆𝑋𝑌𝑍 using its sides and angles.
One angle has a measure that is greater than 90° so the triangle is obtuse. All of
the angles have different measures and the sides have different lengths, so the
triangle is scalene.
Answer: obtuse scalene triangle
14. Classify ∆𝑈𝑉𝑊 using its sides and angles.
The triangle has an obtuse angle and two congruent angles.
Answer: obtuse isosceles triangle
15. Classify ∆𝐷𝐸𝐹 using its sides and angles.
The triangle has a right angle and three sides with different lengths.
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Answer: right scalene triangle
16. Classify ∆𝑅𝑆𝑇 using its sides and angles.
The triangle has a right angle and two sides with the same length and angles with
the same measure.
Answer: right isosceles triangle
17. Classify ∆𝐷𝐸𝐹 using its sides and angles.
The triangle has three acute angles and two sides with the same length and angles
with the same measure.
Answer: acute isosceles triangle
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18. Classify ∆𝐻𝐽𝐾 using its sides and angles.
The angles are all acute and the sides appear to all have different lengths.
Answer: acute scalene triangle
19. Solve for 𝑥 in the figure below.
The sum of the measures of the interior angles of a triangle is 180°, which gives
us the equation 20 + 30 + 𝑚∠𝐴𝐵𝐶 = 180; so 𝑚∠𝐴𝐵𝐶 = 130°. The angle
labeled with 𝑥 is vertical to ∠𝐴𝐵𝐶, so the two angles are congruent. Therefore,
𝑥 = 130°.
Answer: 130°
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20. Solve for 𝑓 in the figure below.
The sum of the measures of the interior angles of a triangle is 180°, which gives
us the equation 57 + 65 + 𝑚∠𝐸𝐹𝐺 = 180; so 𝑚∠𝐸𝐹𝐺 = 58°. Therefore
𝑓 = 58°.
Answer: 58°
21. Solve for 𝑥 in the figure below.
The sum of the measures of the interior angles of a triangle is 180°, which gives
us the equation 54 + 55 + 𝑥 + 74 = 180; 𝑥 + 183 = 180 so 𝑥 = −3.
Answer: −3
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22. Solve for 𝑧 in the figure below.
The sum of the measures of the interior angles of a triangle is 180°, which gives
us the equation 90 + 40 + 𝑧 = 180; 𝑧 + 130 = 180 so 𝑧 = 50°.
Answer: 50°
23. Solve for 𝑥 in the figure below.
The sum of the measures of the interior angles of a triangle is 180°, which gives
us the equation 70 + 60 + 8𝑥 + 2 = 180; 8𝑥 + 132 = 180, 8𝑥 = 48 so 𝑥 = 6.
Answer: 6
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24. Solve for 𝑥 in the figure below.
The sum of the measures of the interior angles of a triangle is 180°, which gives
us the equation 20 + 130 + 𝑥 = 180; 𝑥 + 150 = 180, so 𝑥 = 30.
Answer: 30°
25. Solve for 𝑥 in the figure below.
The figure shows that ∠𝑁 ≅ ∠𝑂. Therefore, 𝑀𝑁̅̅ ̅̅ ̅ ≅ 𝑀𝑂̅̅ ̅̅ ̅, so 𝑥 = 7.
Answer: 7
26. Suppose the measures of a triangle are labeled 𝑥°, 2𝑥°. and 3𝑥°. What are the
measures of the three angles of the triangle?
The sum of the measures of the interior angles of a triangle is 180°, which gives
us the equation 𝑥 + 2𝑥 + 3𝑥 = 180; 6𝑥 = 180, so 𝑥 = 30. Then, 2𝑥 =
60 and 3𝑥 = 90.
Answer: 30°, 60°, 90°
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27. Solve for 𝑥 in the figure below.
The sum of the measures of the interior angles of a triangle is 180° and the figure
shows two congruent sides. This means the base angles are congruent, so
∠𝐸 ≅ ∠𝐹 which gives us the equation 𝑥 + 𝑥 + 40 = 180; 2𝑥 + 40 = 180, 2𝑥 =
140 so 𝑥 = 70.
Answer: 70°
28. Solve for 𝑥 in the figure below.
The figure shows two congruent sides. This means the base angles are congruent,
so ∠𝑅 ≅ ∠𝑆 ; m∠𝑆 = 𝑚∠𝑅 = 75°, so 𝑥 = 75°.
Answer: 75°
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29. Solve for 𝑥 in the figure below.
The sum of the measures of the interior angles of a triangle is 180° and the figure
shows two congruent sides. This means the base angles are congruent, so
∠𝐻 ≅ ∠𝐽 and m∠𝐻 = 𝑚∠𝐽 = 65°. Furthermore, the angle marked 𝑥 is vertical to
the third angle in the triangle, which means the two angles are congruent. This
gives us the equation 65 + 65 + 𝑥 = 180; 𝑥 + 130 = 180, so 𝑥 = 50.
Answer: 50°
30. Solve for 𝑥 in the figure below.
The figure shows an exterior angle of the triangle has a measure of 120°. Then,
the interior angle, next to the exterior angle, and the exterior angle form a
straight angle, so the two angles are supplementary. This means that 𝑚∠𝐶𝐴𝐵 =
60°. The figure also shows two congruent sides. This means the base angles are
congruent, so ∠𝐶 ≅ ∠𝐵 ; so 𝑚∠𝐶 = 𝑚∠𝐵 = 𝑥. Next, the sum of the measures of
the interior angles of a triangle is 180°. This gives us the equation 60 + 𝑥 + 𝑥 =
180, 60 + 2𝑥 = 180, 2𝑥 = 120, so 𝑥 = 60°.
Answer: 60°
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