Step-by-Step Learning
Learn the methods for constructing triangles using given information.
Example 1: Constructing a Triangle (SSS Criterion)
Construct triangle ABC, given AB = 5 cm, BC = 6 cm, and AC = 7 cm.
Step 1: Draw a line segment BC of length 6 cm.
Step 2: With B as the center and radius 5 cm (length of AB), draw an arc.
Step 3: With C as the center and radius 7 cm (length of AC), draw another arc intersecting the previously drawn arc at point A.
Step 4: Join AB and AC.
Result: Triangle ABC is the required triangle.
Example 2: Constructing a Triangle (SAS Criterion)
Construct triangle PQR, given PQ = 4 cm, Angle P = 60 degrees, and PR = 5 cm.
Step 1: Draw a line segment PQ of length 4 cm.
Step 2: At point P, construct an angle of 60 degrees using a protractor or compass. Draw a ray PX along the arm of the angle.
Step 3: With P as the center and radius 5 cm (length of PR), draw an arc intersecting the ray PX at point R.
Step 4: Join QR.
Result: Triangle PQR is the required triangle.
Example 3: Constructing a Triangle (ASA Criterion)
Construct triangle XYZ, given Angle Y = 45 degrees, YZ = 6 cm, and Angle Z = 75 degrees.
Step 1: Draw a line segment YZ of length 6 cm.
Step 2: At point Y, construct an angle of 45 degrees. Draw a ray YA.
Step 3: At point Z, construct an angle of 75 degrees. Draw a ray ZB.
Step 4: The rays YA and ZB will intersect at a point. Label this point X.
Result: Triangle XYZ is the required triangle.
Example 4: Triangle Inequality Theorem
Understand the condition for three side lengths to form a triangle.
Theorem: The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Condition: For three lengths a, b, and c to form a triangle, all three of these inequalities must be true:
- a + b > c
- a + c > b
- b + c > a
Example: Can sides of lengths 3 cm, 4 cm, and 5 cm form a triangle?
- 3 + 4 = 7 > 5 (True)
- 3 + 5 = 8 > 4 (True)
- 4 + 5 = 9 > 3 (True)
Since all three inequalities are true, these lengths can form a triangle (specifically, a right triangle).
Example 2: Can sides of lengths 2 cm, 3 cm, and 6 cm form a triangle?
- 2 + 3 = 5. Is 5 > 6? (False)
Since one inequality is false, these lengths cannot form a triangle.
Practice Mode - Triangle Side Checker
Enter three side lengths to check if they can form a triangle using the Triangle Inequality Theorem.
Note: Enter the three lengths separated by commas (e.g., 3, 4, 5).