Question

For each set of measurements, decide whether or not it is possible to draw a triangle with those measurements. If it is possible, draw the triangle. Side lengths 2 cm, 3 cm, and 4 cm Side lengths 2 cm, 3 cm, and 6 cm Angles 90 degrees, 45 degrees, and 45 degrees Angles 90 degrees , 60 degrees, and 60 degrees

Answer 1

1. Triangle

2. Not a triangle

3. Triangle

4. Not a triangle

Explanation:

Required

Check for valid triangles

Given 3 sides of a triangle: A triangle is valid If the sum of any two sides is greater than the third

1. Sides: 2cm, 3cm and 4cm

To check:

2cm + 3cm > 4cm --- True

2cm + 4cm > 3cm ---- True

3cm + 4cm > 2cm ----- True

The above conditions are true, hence the input values form a triangle.

2. Sides: 2cm, 3cm and 6cm

To check:

2cm + 3cm > 6cm --- False

2cm + 6cm > 3cm ---- True

3cm + 6cm > 2cm ----- True

One of the above conditions is false. Hence, the input values do not form a triangle.

Given the angles of a triangle, their sum must be equal to 180°

3. Angles: 90°, 45° and 45°

Sum = 90° + 45° + 45°

Sum = 180°

This is a valid triangle because the sum equals 180°

4. Angles: 90°, 60° and 60°

Sum = 90° + 60° + 60°

Sum = 210°

This is not a valid triangle because the sum does not equal to 180°

The above conditions are true, hence the input values form a triangle.