Draw two triangles that look similar and label them as ABC and DEF. Label one angle a Theo

Question

sides of both triangles with numerical values such that the triangles are, in fact, similar. The scale factor of the sides needs to be 3/4.

Answer 1

Here are two similar triangles labeled ABC and DEF, with side lengths that reflect a scale factor of \( \frac{3}{4} \).

Triangle ABC

• Angle A = 30°
• Side AB = 8 units
• Side AC = 6 units
• Side BC = 10 units

Triangle DEF

• Angle D = 30° (Corresponding to Angle A)
• Side DE = \( \frac{3}{4} \times 8 = 6 \) units
• Side DF = \( \frac{3}{4} \times 6 = 4.5 \) units
• Side EF = \( \frac{3}{4} \times 10 = 7.5 \) units

Triangle Correspondence

• ABC ↔ DEF
• Angle A ↔ Angle D
• AB ↔ DE
• AC ↔ DF
• BC ↔ EF

Summary of the Triangles

• Triangle ABC:

  • \( AB = 8 \)
  • \( AC = 6 \)
  • \( BC = 10 \)
  • \( \angle A = 30° \)

• Triangle DEF:

  • \( DE = 6 \)
  • \( DF = 4.5 \)
  • \( EF = 7.5 \)
  • \( \angle D = 30° \)

Since the angles are equal and the sides are in the ratio \( \frac{3}{4} \), triangles ABC and DEF are similar by the Angle-Angle (AA) criterion for similarity.