**Math Labs with Activity – Explore the Various Criteria for Congruency of Triangles**

**OBJECTIVE**

To explore the various criteria for congruency of triangles, using a set of triangular cut-outs

**Materials Required**

- A set of triangular cut-outs
- A geometry box.

**Theory**

There are five different criteria for the congruency of triangles.

- SAS criterion
- ASA criterion
- AAS criterion
- SSS criterion
- RHS criterion

**Procedure**

**Step 1:** Place all the triangular cut-outs on a table (as shown in Figure 18.1).

**Step 2:** Measure the sides and angles of each triangular cut-out and record them.

**Step 3:** Applying the various criteria of congruency, select the pairs of triangles which are congruent. Record vour observations.

**Step 4:** Select the set of triangles in which all the three pairs of corresponding angles are equal and check for the congruency by AAA criterion. Record your observations.

**Step 5:** Select the set of triangles in which two pairs of corresponding sides and one pair of corresponding angles (other than the included angle) are equal and check for the congruency by SSA criterion. Record your observations.

**Result**

- The sets of triangles that exhibit any of the five criterion—SAS, ASA, AAS, SSS or RHS form sets of congruent triangles.
- The triangles that exhibit AAA criterion are not congruent.
- The triangles that exhibit SSA criterion are not congruent.

**Remarks:**

- The students must check (by taking more triangular cut-outs) for the congruency of triangles exhibiting various congruency criterion.
- It must be made clear to the students that AAA criterion is a necessary but not a sufficient condition for the triangles to be congruent.

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