Question

Important

Given AABC ~ ADE F, determine the following information.



Determine the measure of LB. Show the work that leads to your answer.





Determine the length of EF. Show the work that leads to your answer.

Answer 1

m∠B = 83°

EF = 10

Explanation:

Two triangles are similar if their corresponding angles are the same size.

Therefore if ΔABC ~ ΔDEF then:

• ∠A ≅ ∠D = 24°
• ∠B ≅ ∠E
• ∠C ≅ ∠F = 73°

Interior angles of a triangle sum to 180°:

⇒ m∠A + m∠B + m∠C = 180°

⇒ 24° + m∠B + 73° = 180°

⇒ m∠B + 97° = 180°

⇒ m∠B = 83°

In similar triangles, corresponding sides are always in the same ratio.

Therefore if ΔABC ~ ΔDEF then:

⇒ AB : DE = BC : EF = CA : FD

⇒ 12 : DE = 8 : EF = 16 : 20

Therefore, to find the length of EF:

`\implies \sf 8 : EF = 16 : 20`

`\implies \sf (8)/(EF) = (16)/(20)`

`\implies \sf 8 \cdot 20= 16 \cdot EF`

`\implies \sf160= 16 \cdot EF`

`\implies \sf EF=(160)/(16)`

`\implies \sf EF=10`