Question

1. Draw acute Δ GHI and acute Δ JKL below to where they look congruent.
2. Write a congruent statement for the two triangles. 3. Label ∠D as 6x + 6, ∠E as x 4x + 8, ∠F as 2x + 12 and ∠B as 3y + 6 4. Solve for x and solve for y.
…

Answer 1

To address the tasks presented, we'll break it down step by step. However, please note that as a text-based AI, I can't physically draw triangles. I will describe how you can visualize the triangles as congruent.

### 1. Drawing Triangles:

You would want to draw two acute triangles, Δ GHI and Δ JKL, adjacent to one another ensuring they are visually congruent (same shape and size). Here is a textual representation of how you might label them:

```
G
/ \
/ \
H-----I

J
/ \
/ \
K-----L
```

Ensure that the corresponding angles and sides are the same in both triangles.

### 2. Congruent Statement:

A congruent statement for the two triangles could be written as:
\[ \Delta GHI \cong \Delta JKL \]

This means that triangle GHI is congruent to triangle JKL.

### 3. Angle Labels:

Based on your provided details, let's label the angles as follows:

- \( \angle D = 6x + 6 \)
- \( \angle E = 4x + 8 \)
- \( \angle F = 2x + 12 \)
- \( \angle B = 3y + 6 \)

### 4. Solve for \( x \) and \( y \):

To solve for \( x \) and \( y \), we'll first use the fact that the sum of angles in a triangle equals 180 degrees. If we have the angles from one triangle:

#### Angle Relationships for Triangle GHI:
- \( \angle D + \angle E + \angle F = 180^\circ \)

Substituting in the values of the angles:
\[
(6x + 6) + (4x + 8) + (2x + 12) = 180
\]
Combining terms:
\[
6x + 4x + 2x + 6 + 8 + 12 = 180
\]
\[
12x + 26 = 180
\]
Now, subtract 26 from both sides:
\[
12x = 154
\]
Divide by 12:
\[
x = \frac{154}{12}
\]
Simplifying:
\[
x = 12.83 \text{ (approx)}
\]

#### Angle Relationships for Triangle JKL:
If you have angles related to \( y \) in triangle JKL, you can also establish a similar equation based on angle sums, assuming \( \angle B \) is part of this triangle should be summed similarly, i.e., \( \angle J + \angle K + \angle L = 180^\circ \).

However, as we don't have specific angle definitions for \( \angle J \), \( \angle K \), and \( \angle L \), let's proceed with \( \angle B = 3y + 6 \):

Assuming \( \angle B \) is also another angle in triangle JKL:
\[
\angle B + \text{(Other Angles)} = 180^\circ
\]

Without loss of generality, if we consider this triangle also has an angle sum equation involving \( y \), you could construct the angle relations accordingly. Once you define \( \angle J \) and \( \angle K \) such that they together with \( B \) sum to 180, you can solve for \( y \).

Please specify the other angles tied to \( y \) for a complete solution if you need assistance calculating \( y \)!