Question

which pairs of triangles are similar?
choose similar or not similar for each pair of triangles.
triangles similar not similar
triangle 1: 27°, 92°
triangle 2: 62°, 27°
triangle 1: 55°, 85°
triangle 2: 85°, 40°
triangle 1: 98°, 35°
triangle 2: 35°, 57°

Explanation:

Step1: Find the third angle of each triangle

The sum of angles in a triangle is \(180^{\circ}\).
For the first pair:

• Triangle 1: Third angle \(=180-(27 + 92)=61^{\circ}\)
• Triangle 2: Third angle \(=180-(62 + 27)=91^{\circ}\)

Since the angles are not equal, they are not similar.

Step2: For the second pair:

• Triangle 1: Third angle \(=180-(55 + 85)=40^{\circ}\)
• Triangle 2: Third angle \(=180-(85 + 40)=55^{\circ}\)

Since the angles are equal (\(55^{\circ},85^{\circ},40^{\circ}\)), they are similar.

Step3: For the third pair:

• Triangle 1: Third angle \(=180-(98 + 35)=47^{\circ}\)
• Triangle 2: Third angle \(=180-(35 + 57)=88^{\circ}\)

Since the angles are not equal, they are not similar.

Answer:

• Triangle 1 (\(27^{\circ},92^{\circ}\)) and Triangle 2 (\(62^{\circ},27^{\circ}\)): Not Similar
• Triangle 1 (\(55^{\circ},85^{\circ}\)) and Triangle 2 (\(85^{\circ},40^{\circ}\)): Similar
• Triangle 1 (\(98^{\circ},35^{\circ}\)) and Triangle 2 (\(35^{\circ},57^{\circ}\)): Not Similar