Question

One triangle has angles that measures 45 degrees and 83 degrees. Another triangle has angles that measure 45 degrees and 42 degrees Are the triangles similar? How do you know?

Answer 1

The two triangles are not similar

Explanation:

Similar triangles have equal corresponding angles and proportion sides

Ex: If Δ ABC is similar to ΔXYZ, then

• m∠A = m∠X, m∠B = m∠Y, m∠C = m∠Z

• 
  `(AB)/(XY)=(BC)/(YZ)=(AC)/(XZ)`

In the given question

∵ One triangle has angles that measure 45° and 83°

→ Find the measure of the 3rd angle

∵ The sum of the measures of the angles of a triangle is 180°

∴ The measure of the 3rd angle = 180° - 45° - 83°

∴ The measure of the 3rd angle = 52°

∴ The measures of the angles of this triangle are 45°, 83°, 52°

∵ Another triangle has angles that measure 45° and 42°

→ Find the measure of the 3rd angle

∴ The measure of the 3rd angle = 180° - 45° - 42°

∴ The measure of the 3rd angle = 93°

∴ The measures of the angles of this triangle are 45°, 93°, 42°

∵ The two triangles have different measures of 2 angles

→ That means their corresponding angles are not equal

∴ The two triangles are not similar