4-1 Practice Classifying Triangles Answer Key (2024)

FAQs

How do you classify each triangle as equilateral isosceles or scalene? ›

In a scalene triangle, all the sides of a triangle are of different length. In an isosceles triangle, two sides of a triangle are of the same measure. In an equilateral triangle, all the sides of a triangle are of equal length.

Equiangular Triangle: A triangle where all the angles are congruent. You can also classify a triangle by its sides. Scalene Triangle: A triangle where all three sides are different lengths. Isosceles Triangle: A triangle with at least two congruent sides.

Right Triangle: When a triangle has one right angle. Obtuse Triangle: When a triangle has one obtuse angle. Acute Triangle: When all three angles in the triangle are acute. Equiangular Triangle: When all the angles in a triangle are congruent.

Solving right triangles

We can use the Pythagorean theorem and properties of sines, cosines, and tangents to solve the triangle, that is, to find unknown parts in terms of known parts. Pythagorean theorem: a² + b² = c². Sines: sin A = a/c, sin B = b/c. Cosines: cos A = b/c, cos B = a/c.

Based on their sides, the 3 triangles are classified as equilateral triangles, isosceles triangles, and scalene triangles. Based on their angles, the 3 types of triangles are listed as, acute triangle, obtuse triangle, and right-angled triangle.

If the square of the longest side is greater than the sum of the squares of the two shorter sides, then the triangle is obtuse at 𝐵 . If the square of the longest side is less than the sum of the squares of the two shorter sides, then the triangle is acute.

a) Since 45 degrees is less than the right angle, it is an acute angle. b) 90 degrees is called a right angle. c) 135 degrees is greater than 90 degrees and an angle that is greater than the right angle (90 degrees) and less than 180 degrees is an obtuse angle. d) 180 degrees is called a straight angle.

If the sum of the squares of the two shorter sides of a triangle is greater than the square of the longest side, the triangle is acute. However, if the sum of the squares of the two shorter sides of a triangle is smaller than the square of the longest side, the triangle is obtuse.

The Pythagorean theorem states that a² + b² = c² in a right triangle where c is the longest side. You can use this equation to figure out the length of one side if you have the lengths of the other two. The figure shows two right triangles that are each missing one side's measure.

Triangular numbers are numbers that make up the sequence 1, 3, 6, 10, . . .. The nth triangular number in the sequence is the number of dots it would take to make an equilateral triangle with n dots on each side. The formula for the nth triangular number is (n)(n + 1) / 2.