Question

answer the question correctly to continue! which pair of triangles is similar? one triangle is isosceles and the other is scalene. one has angles of 40°, 60°, 80°, and the other has 40°, 60°, 80°. one triangle has sides 3, 4, 5 and the other has 6, 9, 12. one triangle is larger than the other.

Explanation:

Step1: Recall the similarity criteria

For two triangles to be similar, their corresponding angles must be equal (AA - Angle - Angle similarity criterion).

Step2: Analyze each option

• Option 1: An isosceles triangle (two equal angles) and a scalene triangle (all angles different) cannot be similar as their angles are not equal.
• Option 2: If one triangle has angles \(40^{\circ},60^{\circ},80^{\circ}\) and the other has \(40^{\circ},60^{\circ},80^{\circ}\), by AA similarity (all three angles equal), the triangles are similar.
• Option 3: For sides \(3,4,5\) and \(6,9,12\), \(\frac{3}{6}=\frac{1}{2}\), \(\frac{4}{9}

eq\frac{1}{2}\), \(\frac{5}{12}
eq\frac{1}{2}\). Since the ratios of corresponding sides are not equal, the triangles are not similar (fails SSS - Side - Side - Side similarity as ratios are not equal).

• Option 4: Just being larger does not imply similarity. Similarity requires either equal - angled (AA) or proportional - sided (SSS, SAS) conditions.

Answer:

One has angles of \(40^{\circ},60^{\circ},80^{\circ}\), and the other has \(40^{\circ},60^{\circ},80^{\circ}\)