Question

State which pair of triangles in the figure given below is similar. Write the similarity criterion used, and also write the pair of similar triangles in symbolic form.

Answer 1

For ΔABC:

• AB = 3 cm
• AC = 4 cm
• ∠A = 50°

For ΔDEF:

• DE = 6 cm
• DF = 8 cm
• ∠D = 50°

Now comparing the sides, including the equal angle:

`(AB)/(DE) = 3/6 = 1/2`,

`(AC)/(DF) = 4/8 = 1/2`

Also,

∠A = ∠D = 50°

Thus, the two sides are proportional, and the included angle is equal.

So, the triangles are similar by the SAS (Side-Angle-Side) similarity criterion.

The pair of similar triangles in symbolic form:

△ABC ∼ △DEF