Question

Make a sketch of each triangle. If it is not possible to sketch the figure, write not possible. obtuse and not isosceles

Short answer

Sketch a triangle with one angle > 90° and all sides of different lengths.

Step-by-step solution

Understanding Triangle Properties

An obtuse triangle has one angle greater than 90 degrees. A non-isosceles triangle is one where no two sides are equal in length.

Sketching the Triangle

To draw an obtuse and not isosceles triangle, ensure that one angle is greater than 90 degrees and all sides are of different lengths. Start by sketching a horizontal line for the base; then, draw two other sides such that one creates an angle greater than 90 degrees with the base.

Key concepts

Triangle Properties

Understanding the properties of triangles is key to identifying and sketching different types of triangles. A triangle is a geometric shape with three sides and three angles. These angles always add up to 180 degrees. Here are some common triangle categories based on side length and angle size:

• Equilateral Triangle: All three sides and angles are equal. Each angle measures 60 degrees.
• Isosceles Triangle: Two sides are of equal length, and the angles opposite these sides are also equal.
• Scalene Triangle: All sides and angles have different measures.
• Acute Triangle: All angles are less than 90 degrees.
• Right Triangle: One angle is exactly 90 degrees.
• Obtuse Triangle: One angle is greater than 90 degrees.

Recognizing these properties helps when sketching or analyzing different triangles. Depending on the problem requirements, a triangle can fit into several categories at once, such as an isosceles right triangle.

Angle Measurement

In any triangle, the measurement of angles is crucial to determine its type and properties. Let's dive into some key points about angle measurement in triangles:

• The sum of the angles in a triangle is always 180 degrees. This is a fundamental rule and applies to all triangles regardless of their shape.
• Each type of triangle has distinct angle characteristics. For example, a right triangle has one 90-degree angle, whereas an obtuse triangle has one angle greater than 90 degrees.

When sketching an obtuse triangle, ensure at least one of the angles is greater than 90 degrees, resulting in two other angles that are less than 90 degrees. This balance is necessary to meet the total of 180 degrees.
An understanding of angle measurements helps in visually distinguishing obtuse triangles from other types and aids in precise sketching or construction.

Isosceles Triangle

An isosceles triangle is known for having two sides of equal length. This unique feature also means the angles opposite those sides are equal, providing visual symmetry. Here are the main aspects:

• Equal Length Sides: In an isosceles triangle, two sides are always equal. This is a defining characteristic, separating it from scalene triangles where no sides are the same length.
• Base Angles: The angles opposite the equal sides are known as base angles and are congruent, meaning they have the same measurement.

Understanding the isosceles triangle is essential in distinguishing it from other types. In particular, when you're tasked with sketching an obtuse and not isosceles triangle, knowing that it cannot have sides of equal length helps you eliminate certain shapes and leads to a more accurate sketch or recognition of the triangle type required.