**Prerequisite:**Students should know how to construct a triangle using protector, compass, and ruler

**Experiment #1:**

Construct five triangles such that**:**

First triangle : A_{1}B_{1} = 8 cm, B_{1}C_{1} = 10 cm, A_{1}C_{1} = 6 cm

Second triangle : A_{2}B_{2} = 4 inches, B_{2}C_{2} = 5 inches, A_{2}C_{2} = 3 inches

Third triangle : A_{3}B_{3} = 6 inches, B_{3}C_{3} = 7.5 inches, A_{3}C_{3} = 4.5 inches

Fourth triangle : A_{4}B_{4} = 12 cm, B_{4}C_{4} = 15 cm, A_{4}C_{4} = 9 cm

Fifth triangle : A_{5}B_{5} = 9.6 cm, B_{5}C_{5} = 12 cm, A_{5}C_{5} = 7.2 cm

**Observation: **

Measure the following angles:

A_{1,} B_{1,} C_{1}

A_{2,} B_{2,} C_{2}

A_{3,} B_{3,} C_{3}

A_{4,} B_{4,} C_{4}

A_{5,} B_{5,} C_{5}

**Inference:**

When we construct two triangles, such that ratio of corresponding sides were same, we observed that corresponding angles were same in these two triangles.

**Experiment #2:**

Construct two triangles such that

First triangle : A_{1}B_{1} = 12 cm, A_{1} = 70 degrees, B_{1} = 60 degrees

Second triangle : A_{2}B_{2} = 06 in., A_{1} = 70 degrees, B_{1} = 60 degrees

Third triangle : A_{3}B_{3} = 10 cm, A_{1} = 70 degrees, B_{1} = 60 degrees

Fourth triangle : A_{4}B_{4} = 05 in., A_{1} = 70 degrees, B_{1} = 60 degrees

Fifth triangle : A_{5}B_{5} = 15 cm, A_{1} = 70 degrees, B_{1} = 60 degrees

**Observation:** Measure the following sides:

, , _{ }

, ,

**Inference:**

When we constructed two triangles such that corresponding angles were same, we observed that corresponding ratios are same.

**Conclusion:**

From Experiment 1 and Experiment2, we can conclude that two triangles with same set of corresponding angles are **similar** to each other i.e. ratios of corresponding sides are same.

We can also mathematically prove this concept.

First triangle : A1B1C1 : A1B1 = 8 cm, B1C1 = 10 cm, A1C1 = 6 cm

Second triangle : A2B2 = 4 inches, B2C2 = 5 inches, A2C2 = 3 inches

Third triangle : A3B3 = 6 inches, B3C3 = 7.5 inches, A3C3 = 4.5 inches

Fourth triangle : A4B4 = 12 cm, B4C4 = 15 cm, A4C4 = 9 cm

Fifth triangle : A5B5 = 9.6 cm, B5C5 = 12 cm, A5C5 = 7.2 cm