Classifying and Identifying Triangles

Every angle is small (less than 90°) → acute triangle.

The triangle has two equal angles (50° each) and one angle (80°) that is less than 90°. This makes it an isosceles triangle. Since all angles are less than 90°, it is classified as an acute triangle, thus it is an acute isosceles triangle.

A right isosceles triangle is defined by having one right angle (90 degrees) and two sides that are equal in length.

The triangle has two sides of equal length (10 and 10), which classifies it as isosceles. Since the side lengths also satisfy the triangle inequality and the angle opposite the longest side (14) is less than 90 degrees, it is an isosceles acute triangle.

For three angles to form a triangle, their measures must sum up to exactly 180°. In option D, the angles are 100°, 40°, and 50°, which sum to 190° (100° + 40° + 50° = 190°). Since this exceeds 180°, these angles cannot form a triangle. The other options sum to 180° or less, making them valid combinations for triangle formation.

For a set of angles to form a valid triangle, the sum of the angles must equal 180°. In option B, the angles sum to 90° + 45° + 45° = 180°, making it a valid triangle. The other options do not satisfy this condition.

Triangle inequality:

• 5,5,10 fails (sum equals largest).


• 7,8,15 fails (sum equals largest).


• 9,9,5 works (each pair sums greater).


• 2,2,5 fails (sum less than largest).

Add the two shorter sides: 4 + 7 = 11.

They must add to more than the third side — they don’t.

So, no triangle forms.

Two sides are equal → that’s an isosceles triangle.

Right triangle with all angles different means Right scalene.

In a triangle, the sum of the interior angles is always 180°. If two angles measure 45° each, their sum is 90°. Therefore, the third angle must be 180 - 90 = 90°.

All three sides are the same → all angles are 60°.

So, it’s an equilateral triangle.

Having a 90° angle makes it a right triangle.

An angle greater than 90° makes it obtuse.

Three different sides means scalene.

In the SSA condition, when the angle size isn’t given, we can’t tell if 0, 1, or 2 triangles form → Not enough information.

8² + 15² = 64 + 225 = 289 = 17² → right triangle.

In the SSA (side-side-angle) condition, when two sides and a nonincluded angle are known, two different triangles can form — this is called the ambiguous case.

In the SAS (side-angle-side) condition, when two sides and their included angle are known, only one unique triangle can be formed.

All equal sides means equilateral, which is always acute (all 60°)