Math Problem Statement

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A triangle, ABC, has angle measures of 40°, 40°, and 100° and exactly two congruent (equal) sides. How would this triangle be classified?

Solution

The triangle in the image has two equal angles (40°, 40°) and one larger angle (100°). The triangle has two congruent sides, which means it is an isosceles triangle.

Now, considering the angles:

  • The 100° angle is greater than 90°, so this makes the triangle obtuse.

Thus, the triangle is classified as an Isosceles obtuse triangle.

Would you like further explanation on this? Let me know if you have any questions!

Here are 5 related questions to explore:

  1. What are the properties of an isosceles triangle?
  2. What is the sum of the angles in any triangle?
  3. How do you classify triangles based on angle size (acute, obtuse, right)?
  4. What makes a triangle isosceles versus scalene?
  5. Can a triangle have more than one obtuse angle?

Tip: Always remember that the sum of the interior angles of any triangle is always 180°.

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Math Problem Analysis

Mathematical Concepts

Triangle Classification
Angles
Isosceles Triangles
Types of Angles

Formulas

Sum of angles in a triangle = 180°

Theorems

Triangle Angle Sum Theorem
Isosceles Triangle Properties

Suitable Grade Level

Grades 6-8