Question

If ∆𝐴𝐵𝐶 and ∆𝐿𝑀𝑁 are similar, find the missing sides and angles.

• A. AC = 2.17 cm, ∠A = 50°, LM = 2 cm, ∠M = 70°
• B. AC = 2.17 cm, ∠A = 50°, LM = 4 cm, ∠M = 50°
• C. AC = 2.17 cm, ∠A = 70°, LM = 4 cm, ∠M = 50°
• D. AC = 2.17 cm, ∠A = 50°, LM = 4 cm, ∠M = 70°

Answer 1

The correct option is D AC = 2.17 cm, ∠A = 50°, LM = 4 cm, ∠M = 70°

∆ABC and ∆LMN are similar.

Similar triangles have the same corresponding angle measures and proportional side lengths.

Therefore,
∠A = 50°, ∠M = 70° (from the figure)

$\frac{AB}{LM}=\frac{BC}{MN}=\frac{CA}{NL}$ (side ratio)

$\frac{2}{LM}=\frac{1.76}{3.52}=\frac{CA}{4.34}=\frac{1}{2}$

$LM=4$ cm and $CA=2.17$ cm

Answer: AC = 2.17 cm, ∠A = 50°, LM = 4 cm, ∠M = 70°