Answer – An isosceles acute triangle is one in which at least two angles (and the sides opposite them) are equal and all angles measure less than 90°. An example of such a triangle would be one with angles 48°, 48°, and 84°.

Explanation:

In Geometry, an isosceles acute triangle has the following defining properties:

  • It has two equal angles.
  • It has two equal sides (which are opposite the equal angles).
  • It has a minimum of two acute angles (measuring less than 90°).

Thus, it possesses the properties of both an isosceles triangle as well as an acute triangle.

Below is an illustration of an isosceles acute triangle.

Isoceles acute triangle ABC with equal sides AB and AC and equal angles B and C

Not all isosceles triangles are acute. Since the two properties (isosceles and acute) are independent of one another, isosceles triangles can also be obtuse (with one angle measuring more than 90°). An example of an isosceles obtuse triangle would be one with angles 110°, 35°, and 35°.

Popular Questions

  • An altitude is drawn from the vertex of an isosceles triangle, forming a right angle and two congruent triangles. As a result, the altitude cuts the base into two equal segments. The length of the altitude is 29 inches, and the length of the base is 18 inches. Find the triangle’s perimeter. Round to the nearest tenth of an inch.

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