Triangle ABC is similar to triangle QRS. The triangles are shown with side lengths in centimeters.

Answer 1

To determine the relationships between the side lengths of triangles ABC and QRS, you can use the properties of similar triangles. When two triangles are similar, the ratios of their corresponding side lengths are equal.

Here's how you can approach the problem:

1. Identify Corresponding Sides: Determine which sides of triangle ABC correspond to which sides of triangle QRS. For example, if side AB corresponds to side QR, side BC corresponds to side RS, and side CA corresponds to side SQ.

2. Use the Side Ratios: If you know the lengths of the sides of triangle ABC (say a, b, c) and the sides of triangle QRS (say p, q, r), you can set up ratios: \[ \frac{AB}{QR} = \frac{BC}{RS} = \frac{CA}{SQ} \]

3. Calculate Unknown Side Lengths: If you have some lengths and need to find others, you can rearrange the ratios to solve for unknowns. For instance, if you want to find a side length in triangle QRS using the known side lengths of triangle ABC, you would rearrange the ratio: \[ QR = \frac{AB \cdot RS}{BC} \]

4. Check the Scale Factor: The scale factor of similarity can be calculated as well by dividing one of the sides of triangle ABC by the corresponding side of triangle QRS. This will give you a consistent ratio that applies to all sides.

If you provide the specific side lengths of each triangle or any additional information about the triangles, I can help you with more detailed calculations or conclusions.

Answer 2

What’s the answer and solve it

Answer 3

To provide an answer and solve the problem, I'll need the specific side lengths of triangles ABC and QRS. Since I don't have that information, let me illustrate how to solve such a problem with an example.

Example Problem

Suppose:

• Triangle ABC has side lengths:

  • \( AB = 6 , \text{cm} \)
  • \( BC = 8 , \text{cm} \)
  • \( CA = 10 , \text{cm} \)

• Triangle QRS has side lengths:

  • \( QR = 9 , \text{cm} \)
  • \( RS = ? \)
  • \( SQ = ? \)

Solution Step-by-Step

1. Determine Corresponding Side Lengths:

   • Let's correspond them as follows:
     • \( AB \) corresponds to \( QR \)
     • \( BC \) corresponds to \( RS \)
     • \( CA \) corresponds to \( SQ \)

2. Set Up Ratios: Using the known sides: \[ \frac{AB}{QR} = \frac{BC}{RS} = \frac{CA}{SQ} \] Plugging in the values we have: \[ \frac{6}{9} = \frac{8}{RS} = \frac{10}{SQ} \]

3. Calculate the Scale Factor: \[ \frac{6}{9} = \frac{2}{3} \] This means that the sides of triangle QRS are \(\frac{2}{3}\) the size of triangle ABC.

4. Find \( RS \): To find \( RS \): \[ \frac{8}{RS} = \frac{2}{3} \] Cross-multiplying gives: \[ 2 \cdot RS = 3 \cdot 8 \] \[ 2 \cdot RS = 24 \] \[ RS = \frac{24}{2} = 12 , \text{cm} \]

5. Find \( SQ \): To find \( SQ \): \[ \frac{10}{SQ} = \frac{2}{3} \] Cross-multiplying gives: \[ 2 \cdot SQ = 3 \cdot 10 \] \[ 2 \cdot SQ = 30 \] \[ SQ = \frac{30}{2} = 15 , \text{cm} \]

Final Result

• Lengths of triangle QRS:
  • \( QR = 9 , \text{cm} \)
  • \( RS = 12 , \text{cm} \)
  • \( SQ = 15 , \text{cm} \)

If you provide the actual side lengths of triangles ABC and QRS, I can apply the same method with those specific numbers!