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?

<p>Scalene triangle (D)</p> 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?

<p>20° (C)</p> Signup and view all the answers

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

<p>60° (B)</p> 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?

<p>12 cm (B)</p> 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?

<p>It is an isosceles triangle (C)</p> 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

<p>Obtuse Scalene (A)</p> Signup and view all the answers

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

<p>Right Isosceles (C)</p> Signup and view all the answers

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

<p>Equilateral (D)</p> 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

<p>Obtuse Scalene (A)</p> 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.

<p>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.</p> Signup and view all the answers

In the figure, m∠1 = ______ degrees.

<p>68</p> Signup and view all the answers

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

<p>6</p> Signup and view all the answers

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

<p>5.5</p> Signup and view all the answers

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

<p>1</p> Signup and view all the answers

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

<p>60</p> Signup and view all the answers

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

<p>4</p> Signup and view all the answers

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

<p>7</p> 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 = ______

<p>6</p> 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

<p>40</p> 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 = ______

<p>2</p> 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 = ______

<p>7</p> 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

<p>17</p> Signup and view all the answers

Flashcards

Classify a triangle by angles

Determine if a triangle is acute, obtuse, or right based on its angle measures.

Classify a triangle by sides

Determine if a triangle is equilateral, isosceles, or scalene based on the lengths of its sides.

Calculate the distance between two points

Find the length of a line segment connecting two points in a coordinate plane using the distance formula.

Find missing angle measures

Determine unknown angles in a triangle, given other angle measurements.

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Solve for x in a triangle problem

Find the value of the unknown variable 'x' in a triangle, given angle or side relationships.

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Solve for missing measures in a triangle problem

Find the lengths of unknown sides or the measures of unknown angles given certain information about a triangle.

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Equilateral triangle

A triangle with all three sides having equal length.

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Scalene triangle

A triangle with all three sides having different lengths.

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Acute triangle

A triangle where all three angles measure less than 90 degrees.

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Obtuse triangle

A triangle with one angle that measures greater than 90 degrees.

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Right triangle

A triangle with one angle measuring exactly 90 degrees.

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Isosceles triangle

A triangle with two sides of equal length.

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Find x in a triangle equation

Find the value of the unknown variable 'x' in a triangle, given angle or side relationships.

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Solve for missing measures

Find the lengths of unknown sides or the measures of unknown angles given certain information about a triangle.

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Distance formula

A formula used to calculate the distance between two points in a coordinate plane. The formula is: √[(x₂ - x₁)² + (y₂ - y₁)²] where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

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Angle sum property

The sum of the interior angles of any triangle is always 180 degrees.

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Triangle Inequality Theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

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What is the sum of the angles in a triangle?

The sum of the interior angles of any triangle is always 180 degrees.

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What is a triangle with three equal sides?

A triangle with all three sides having equal length is called an equilateral triangle.

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What makes a triangle isosceles?

A triangle with two sides of equal length is called an isosceles triangle.

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What is a triangle with all different sides called?

A triangle with all three sides having different lengths is called a scalene triangle.

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What is the angle measurement in a right triangle?

A right triangle has one angle measuring exactly 90 degrees.

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How many degrees are in an acute triangle?

All three angles in an acute triangle measure less than 90 degrees.

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What is the key characteristic of an obtuse triangle?

An obtuse triangle has one angle that measures greater than 90 degrees.

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What is the Pythagorean Theorem?

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

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What is a midpoint?

The midpoint of a line segment is the point that divides the segment into two equal parts.

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How do you find the midpoint of a line segment?

The midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is found using the midpoint formula: ((x₁ + x₂)/2, (y₁ + y₂)/2).

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How do you determine if a triangle is a right triangle?

A triangle is a right triangle if and only if the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the lengths of the other two sides. This is the Pythagorean Theorem.

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What is the relationship between angles in a triangle and its sides?

In a triangle, the angle opposite the longest side is the largest angle, and the angle opposite the shortest side is the smallest angle. Conversely, the side opposite the largest angle is the longest side, and the side opposite the smallest angle is the shortest side.

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What does it mean to solve for x in a triangle equation?

Solving for 'x' in a triangle equation means finding the value of the unknown variable 'x' that satisfies the given relationship between angles or sides in the triangle.

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What are the properties of an equilateral triangle?

An equilateral triangle has three equal sides and three equal angles, each measuring 60 degrees.

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What are the properties of an isosceles triangle?

An isosceles triangle has two equal sides and two equal angles.

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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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