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**Homework 3 Isosceles And Equilateral Triangles Answers speama**

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3. ∆FEG is an equilateral triangle. 4. ∆FEG is an isosceles triangle. 5. ∆ABC is an equilateral triangle. Step 6: Solution/Discussion ▪ 6. From ∆AEC, it is easy to deduce that ∆EAD is also an equilateral triangle. This is so because ∆EAD is an isosceles triangle with sides ∆AC and ∆EA of the same length. Therefore, ∆EAD has three equal sides. Moreover, ∆EAD is an equilateral triangle, and so it has three equal angles of measure ∠CDE = ∠CEA. Because there are three equal angles, the triangle is equilateral. Question/Answer/Step-by-step explanation: 6. Since ∆AEC is an equilateral triangle, so is ∆EAD. The sides ∆AC and ∆EA of ∆EAD are of the same length, so ∆EAD is an isosceles triangle. Because there are three equal angles, ∆EAD is an equilateral triangle. Problem 10 A farmer's wife has two sons and one daughter. For her own sake, she wants her daughter to be the oldest, and for the sake of her sons she would like the daughter to be the youngest. How old are her daughters? Note/Step-by-step explanation: 1. 2. Let the difference between the ages of the oldest and the youngest be Δ.. 3. We have Δ = 1 − 2. 4. The farmer's wife, however, would like the difference to be 1. In order to achieve this, we would have to add 1 to both sides of the equation to get 1 − 2 = 1 + 1. However, we cannot add 1 + 1 to both sides of an equation. So, the farmer's wife would have to change the original equation to 1 − 2 = 1. 5. Now, 1 − 2 = 1 would be 1 − 2 + 2, which means that Δ = 1 + 2. Because Δ = 1 + 2, we have ∆ = 2. 7. ∆ABC is a triangle, and so we have ∆BAC = ∆CAB.

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