Question

1. Draw acute Δ ABC and acute Δ DEF below to where they look congruent.
2. Write a congruent statement for the two triangles. 3. Label ∠D as 5x - 2, ∠E as 9x + 3, ∠F as 11x-21, and ∠B as 5y + 35 4. Solve for x and solve for y.

Answer 1

**1. Drawing Acute Triangles**:

Unfortunately, I cannot draw or provide visual content directly. However, I can guide you on how to create two congruent acute triangles, ΔABC and ΔDEF.

To draw two congruent acute triangles:
- Draw triangle ΔABC with the following vertices:
- A(1, 3)
- B(3, 7)
- C(5, 3)

- For triangle ΔDEF, draw it in the same shape and position:
- D(1, 3)
- E(3, 7)
- F(5, 3)

Make sure that both triangles have the same corresponding angles and side lengths, ensuring they look congruent.

**2. Write a congruent statement for the two triangles:**

The congruence statement can be written as:
\[ \Delta ABC \cong \Delta DEF \]

**3. Label the angles:**

- Label the angles as follows:
- ∠B = \(5y + 35\)
- ∠D = \(5x - 2\)
- ∠E = \(9x + 3\)
- ∠F = \(11x - 21\)

Since triangles ΔABC and ΔDEF are congruent, their corresponding angles are equal.

This gives us the following equations based on the corresponding angles:
1. \( \angle D = \angle B \)
\[
5x - 2 = 5y + 35
\]

2. \( \angle E = \angle F \)
\[
9x + 3 = 11x - 21
\]

**4. Solving for x and y:**

### Solving for \(x\):
From the second equation:
\[
9x + 3 = 11x - 21
\]
Subtract \(9x\) from both sides:
\[
3 = 2x - 21
\]
Add 21 to both sides:
\[
24 = 2x
\]
Divide by 2:
\[
x = 12
\]

### Solving for \(y\):
Now substituting \(x = 12\) into the first equation:
\[
5(12) - 2 = 5y + 35
\]
\[
60 - 2 = 5y + 35
\]
\[
58 = 5y + 35
\]
Subtract 35 from both sides:
\[
23 = 5y
\]
Divide by 5:
\[
y = \frac{23}{5} = 4.6
\]

**Final values:**
- \(x = 12\)
- \(y = 4.6\)

Feel free to check these solutions in the original angle equations to ensure accuracy!