Geometry Tutor Worksheet 5 Types of Triangles · shows two congruent sides. This means the base angles are congruent, so ∠ ≅∠ and m∠ =𝑚∠ =65°. Furthermore, the angle

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Geometry Tutor

Worksheet 5

Types of Triangles


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.


7. Classify ∆𝐴𝐵𝐶 using its sides and angles.

8. Classify ∆𝐷𝐸𝐹 using its sides and angles.

9. Classify ∆𝐺𝐻𝐽 using its sides and angles.




12. Classify ∆𝐹𝐸𝐺 using its sides and angles.


13. Classify ∆𝑋𝑌𝑍 using its sides and angles.

14. Classify ∆𝑈𝑉𝑊 using its sides and angles.



16. Classify ∆𝑅𝑆𝑇 using its sides and angles.


18. Classify ∆𝐻𝐽𝐾 using its sides and angles.


19. Solve for 𝑥 in the figure below.

20. Solve for 𝑓 in the figure below.



22. Solve for 𝑧 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?







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



The triangle has a 90° angle which is a right angle. The other angles both have

different measures.

Answer: right scalene triangle


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


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


The triangle has a right angle and two congruent angles.

Answer: right isosceles triangle



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


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


The triangle has a right angle and three sides with different lengths.


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


The triangle has three acute angles and two sides with the same length and angles

with the same measure.

Answer: acute isosceles triangle


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


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°


20. Solve for 𝑓 in the figure below.


us the equation 57 + 65 + 𝑚∠𝐸𝐹𝐺 = 180; so 𝑚∠𝐸𝐹𝐺 = 58°. Therefore

𝑓 = 58°.

Answer: 58°



us the equation 54 + 55 + 𝑥 + 74 = 180; 𝑥 + 183 = 180 so 𝑥 = −3.

Answer: −3


22. Solve for 𝑧 in the figure below.


us the equation 90 + 40 + 𝑧 = 180; 𝑧 + 130 = 180 so 𝑧 = 50°.

Answer: 50°



us the equation 70 + 60 + 8𝑥 + 2 = 180; 8𝑥 + 132 = 180, 8𝑥 = 48 so 𝑥 = 6.

Answer: 6




us the equation 20 + 130 + 𝑥 = 180; 𝑥 + 150 = 180, so 𝑥 = 30.

Answer: 30°


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?


us the equation 𝑥 + 2𝑥 + 3𝑥 = 180; 6𝑥 = 180, so 𝑥 = 30. Then, 2𝑥 =

60 and 3𝑥 = 90.

Answer: 30°, 60°, 90°



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°


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°



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°


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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Geometry Tutor Worksheet 5 Types of Triangles · shows two congruent sides. This means the base angles are congruent, so ∠ ≅∠ and m∠ =𝑚∠ =65°. Furthermore, the angle