Grade 6 Triangles and their Properties
Interactive step-by-step solver for understanding triangles and their properties.
Interactive step-by-step solver for understanding triangles and their properties.
Learn about triangles and their properties through these example problems with detailed step-by-step solutions.
A triangle has sides of 5 cm, 5 cm, and 6 cm. Classify the triangle by its sides.
Sides are 5 cm, 5 cm, and 6 cm.
Sum of any two sides must be greater than the third side:
5 + 5 > 6 (10 > 6, true),
5 + 6 > 5 (11 > 5, true),
5 + 6 > 5 (11 > 5, true).
Since two sides are equal (5 cm = 5 cm), the triangle is isosceles.
A triangle has angles of 40°, 60°, and 80°. Classify the triangle by its angles.
Angles are 40°, 60°, and 80°.
\( 40^\circ + 60^\circ + 80^\circ = 180^\circ \), which is true.
All angles are less than 90° (40°, 60°, 80°), so the triangle is acute-angled.
A triangle has angles of 50° and 70°. Find the third angle.
Angles are 50° and 70°.
The sum of angles in a triangle is \( 180^\circ \).
\( \text{Third angle} = 180^\circ - (\text{Angle 1} + \text{Angle 2}) \).
\( \text{Third angle} = 180^\circ - (50^\circ + 70^\circ) = 180^\circ - 120^\circ = 60^\circ \).
A triangle has two interior angles of 40° and 60°. Find the exterior angle adjacent to the third angle.
Interior angles are 40° and 60°.
An exterior angle equals the sum of the two non-adjacent interior angles.
\( \text{Exterior angle} = 40^\circ + 60^\circ = 100^\circ \).
Third angle = \( 180^\circ - (40^\circ + 60^\circ) = 80^\circ \).
Exterior angle = \( 180^\circ - 80^\circ = 100^\circ \), which matches.
Design a triangular garden with sides 3 m, 4 m, and 5 m. Classify the triangle.
Sides are 3 m, 4 m, and 5 m.
3 + 4 > 5 (7 > 5, true),
3 + 5 > 4 (8 > 4, true),
4 + 5 > 3 (9 > 3, true).
All sides are different (3 ≠ 4 ≠ 5), so the triangle is scalene.
\( 3^2 + 4^2 = 9 + 16 = 25 \), and \( 5^2 = 25 \).
Since \( 3^2 + 4^2 = 5^2 \), the triangle is right-angled.
Enter your own triangle problem, and get a step-by-step solution.
Note: This solver handles classifying triangles by sides (e.g., Sides 5 cm, 5 cm, 6 cm; classify triangle by sides), classifying by angles (e.g., Angles 40°, 60°, 80°; classify triangle by angles), finding the third angle (e.g., Angles 50°, 70°; find third angle), finding an exterior angle (e.g., Interior angles 40°, 60°; find exterior angle), and real-world problems (e.g., Sides 3 m, 4 m, 5 m; classify triangle). Enter the problem clearly.
Use formats like 'Sides 5 cm, 5 cm, 6 cm; classify triangle by sides', 'Angles 40°, 60°, 80°; classify triangle by angles', 'Angles 50°, 70°; find third angle', 'Interior angles 40°, 60°; find exterior angle', or 'Sides 3 m, 4 m, 5 m; classify triangle'.