Triangle Classification Quiz

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Questions and Answers

If triangle PQR has angles measuring 30°, 90°, and 60°, how is it categorized by its angles?

Equilateral triangle

Acute triangle

Right triangle (correct)

Obtuse triangle

Given triangle XYZ with sides measuring 5 cm, 5 cm, and 8 cm, what type of triangle is it based on its sides?

Equilateral triangle

Isosceles triangle (correct)

Acute triangle

Scalene triangle

What is the classification of triangle ABC if it contains one angle that measures 120°?

Obtuse triangle (correct)

Right triangle

Acute triangle

Equilateral triangle

If triangle DEF has sides measuring 9 cm, 12 cm, and 15 cm, what is the classification of the triangle?

Scalene triangle Signup and view all the answers

To find the missing angle in triangle GHI where angles A = 40° and B = 100°, what is the measure of angle C?

20° Signup and view all the answers

What is the value of x in the triangle with angles measuring x, x + 30°, and x + 50°?

60° Signup and view all the answers

If two sides of a triangle measure 7 cm and 10 cm, which of the following could be the length of the third side?

12 cm Signup and view all the answers

What can be determined if triangle JKL has one angle measuring 90° and the other two sides are equal?

It is an isosceles triangle Signup and view all the answers

Classify the triangle by its angles and sides: 26 degrees, 2.5, 2.5, 128 degrees, 26 degrees, 4.5

Obtuse Scalene Signup and view all the answers

Classify the triangle by its angles and sides: 45 degrees, 4.8, 4.8, 45 degrees, 6.8

Right Isosceles Signup and view all the answers

Classify the triangle by its angles and sides: 60 degrees, 8.6, 8.6, 60 degrees, 8.6

Equilateral Signup and view all the answers

Classify the triangle by its angles and sides: 45 degrees, 6.1, 8.7, 79 degrees, 7.4, 44 degrees

Obtuse Scalene Signup and view all the answers

Given points Q(-2, -1), R(1, 5) and S(-8, -4), classify triangle QRS by its sides. Show all work to justify your answer.

QR = \sqrt{(1 - (-2))^2 + (5 - (-1))^2} = \sqrt{3^2 + 6^2} = \sqrt{45} = 3\sqrt{5}, RS = \sqrt{(-8 - 1)^2 + ( - 4 - 5)^2} = \sqrt{(-9)^2 + (-9)^2} = \sqrt{162} = 9\sqrt{2}, QS = \sqrt{(-8 - (-2))^2 + (-4 - (-1))^2} = \sqrt{(-6)^2 + (-3)^2} = \sqrt{45} = 3\sqrt{5}. Therefore, triangle QRS is an isosceles triangle because QR = QS. Signup and view all the answers

In the figure, m∠1 = ______ degrees.

68 Signup and view all the answers

Solve for x in the figure (6x - 23) degrees, (3x - 1) degrees, (8x - 17) degrees: x = ______

6 Signup and view all the answers

Solve for x in the figure (2x + 22) degrees, (9x - 15) degrees, (4x + 11) degrees. x = ______

5.5 Signup and view all the answers

In triangle ABC, which is equilateral, solve for x in (17x - 8) degrees: x = ______

1 Signup and view all the answers

In triangle ABC, which is equilateral, solve for m∠A: m∠A = ______ degrees

60 Signup and view all the answers

In triangle RST, which is isosceles, solve for x in (6x - 23) degrees, (4x + 9) degrees: x = ______

4 Signup and view all the answers

In triangle RST, which is isosceles, solve for m∠X: m∠X = ______ degrees

7 Signup and view all the answers

In triangle PQR, m∠P = 9x - 16, m∠Q = 3x + 11, and m∠R = 7x - 5. Solve for x: x = ______

6 Signup and view all the answers

In triangle PQR, m∠P = 9x - 16, m∠Q = 3x + 11, and m∠R = 7x - 5. Solve for m∠P: m∠P = ______ degrees

40 Signup and view all the answers

In triangle RST, ∠S = ∠T, RS = 9x - 13, ST = 12x + 1, and RT = 4x + 2. Solve for x: x = ______

2 Signup and view all the answers

In triangle ACD, AC = AD, m∠A = 3x - 4, m∠C = 5x + 1, and m∠D = 7x - 27. Solve for x: x = ______

7 Signup and view all the answers

In triangle ACD, AC = AD, m∠A = 3x - 4, m∠C = 5x + 1, and m∠D = 7x - 27. Solve for m∠A: m∠A = ______ degrees

17 Signup and view all the answers

Study Notes

Classifying Triangles by Sides and Angles

Triangle Classification by Angles:
- Acute triangle: All angles are less than 90 degrees.
- Obtuse triangle: One angle is greater than 90 degrees.
- Right triangle: One angle is exactly 90 degrees.
Triangle Classification by Sides:
- Scalene triangle: All sides have different lengths.
- Isosceles triangle: At least two sides have the same length.
- Equilateral triangle: All three sides have the same length.

Triangle Classification by Angles and Sides - Example Problems (1-4)

Problem 1: Illustrates a triangle with two equal sides and angles. Classify by angle and side.
Problem 2: Illustrates a triangle with different side lengths. Classify by angle and side.
Problem 3: Illustrates an isosceles triangle. Note the angles. Identify by side and angle measure.
Problem 4: Illustrates a right triangle that is also isosceles. Indicate its characteristics.

Classifying a Triangle by its Sides (Problem 5)

Given: Coordinates of vertices Q, R, and S of triangle QRS: Q(-2, -1), R(1, 5), S(-8, -4).
Find: Length of each side (QR, RS, QS) and classify triangle QRS by its sides.
Steps: Calculate the distance between each pair of points using the distance formula.
Classification: Based on calculated lengths, determine if the triangle is scalene, isosceles, or equilateral.

Finding Missing Angle Measures (Problems 6-7)

Method: Use angle relationships (adjacent angles, vertically opposite angles, angles on a straight line) along with the properties of triangles (angle sum of a triangle) and parallel lines.
Key Concepts:
- Angles on a straight line add up to 180°
- Vertically opposite angles are equal
- The sum of the angles in a triangle is 180°
Problem Solving: Find unknown angles.

Solving for 'x' and Missing Measures (Problems 8-14)

Problems: Use triangle properties, including the properties of the isosceles triangle in these problems.
Equilateral Triangle (Q10): All sides and angles are equal.
Isosceles Triangle (Q11): At least two sides or angles are equal.
Triangle Angle Sum (Q12): Sum of the angles in a triangle equal 180°.
Other Problems Use the sum of angles, and specific relationships in triangles.
Variable Solving: Finding the value of x in the given equations.
Example: Problem 14 involves solving an algebraic equation to find x. This is followed by using x to find unknown angles within the triangle.

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Test your knowledge on classifying triangles by their sides and angles. This quiz includes example problems that require identifying triangle types based on given characteristics. Perfect for geometry students looking to reinforce their understanding of triangle classification.

Triangle Classification Quiz

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Questions and Answers

If triangle PQR has angles measuring 30°, 90°, and 60°, how is it categorized by its angles?

Given triangle XYZ with sides measuring 5 cm, 5 cm, and 8 cm, what type of triangle is it based on its sides?

What is the classification of triangle ABC if it contains one angle that measures 120°?

If triangle DEF has sides measuring 9 cm, 12 cm, and 15 cm, what is the classification of the triangle?

To find the missing angle in triangle GHI where angles A = 40° and B = 100°, what is the measure of angle C?

What is the value of x in the triangle with angles measuring x, x + 30°, and x + 50°?

If two sides of a triangle measure 7 cm and 10 cm, which of the following could be the length of the third side?

What can be determined if triangle JKL has one angle measuring 90° and the other two sides are equal?

Classify the triangle by its angles and sides: 26 degrees, 2.5, 2.5, 128 degrees, 26 degrees, 4.5

Classify the triangle by its angles and sides: 45 degrees, 4.8, 4.8, 45 degrees, 6.8

Classify the triangle by its angles and sides: 60 degrees, 8.6, 8.6, 60 degrees, 8.6

Classify the triangle by its angles and sides: 45 degrees, 6.1, 8.7, 79 degrees, 7.4, 44 degrees

Given points Q(-2, -1), R(1, 5) and S(-8, -4), classify triangle QRS by its sides. Show all work to justify your answer.

In the figure, m∠1 = ______ degrees.

Solve for x in the figure (6x - 23) degrees, (3x - 1) degrees, (8x - 17) degrees: x = ______

Solve for x in the figure (2x + 22) degrees, (9x - 15) degrees, (4x + 11) degrees. x = ______

In triangle ABC, which is equilateral, solve for x in (17x - 8) degrees: x = ______

In triangle ABC, which is equilateral, solve for m∠A: m∠A = ______ degrees

In triangle RST, which is isosceles, solve for x in (6x - 23) degrees, (4x + 9) degrees: x = ______

In triangle RST, which is isosceles, solve for m∠X: m∠X = ______ degrees

In triangle PQR, m∠P = 9x - 16, m∠Q = 3x + 11, and m∠R = 7x - 5. Solve for x: x = ______

In triangle PQR, m∠P = 9x - 16, m∠Q = 3x + 11, and m∠R = 7x - 5. Solve for m∠P: m∠P = ______ degrees

In triangle RST, ∠S = ∠T, RS = 9x - 13, ST = 12x + 1, and RT = 4x + 2. Solve for x: x = ______

In triangle ACD, AC = AD, m∠A = 3x - 4, m∠C = 5x + 1, and m∠D = 7x - 27. Solve for x: x = ______

In triangle ACD, AC = AD, m∠A = 3x - 4, m∠C = 5x + 1, and m∠D = 7x - 27. Solve for m∠A: m∠A = ______ degrees

Study Notes

Classifying Triangles by Sides and Angles

Triangle Classification by Angles and Sides - Example Problems (1-4)

Classifying a Triangle by its Sides (Problem 5)

Finding Missing Angle Measures (Problems 6-7)

Solving for 'x' and Missing Measures (Problems 8-14)

Studying That Suits You

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