Question

Question

Use the image to answer the question. Two quadrilaterals, upper A (-6,1) upper B (-3,1) upper C (-2,3) upper D (-5,3) and upper E (2,3) upper F (5, 3) upper G (6,5) upper H (3,5), are graphed on a coordinate plane. The x-axis ranges from negative 7 to 7 in increments of 1. The y-axis ranges from negative 3 to 8 in increments of 1. Assess parallelograms ADCB and EHGF to decide if they are congruent. (1 point) Responses which answer is correct and why by solving it whether a b c or d is the true correct answer
Yes, ADCB≅EHGF because parallelogram ADCB was rotated. Yes, upper A upper D upper C upper B congruent to upper E upper H upper G upper F because parallelogram upper A upper D upper C upper B was rotated. Yes, ADCB≅EHGF because parallelogram ADCB was reflected. Yes, upper A upper D upper C upper B congruent to upper E upper H upper G upper F because parallelogram upper A upper D upper C upper B was reflected. Yes, ADCB≅EHGF since parallelogram ADCB was translated. Yes, upper A upper D upper C upper B congruent to upper E upper H upper G upper F since parallelogram upper A upper D upper C upper B was translated. No, ADCB is not congruent to EHGF because parallelogram ADCB was dilated. No, upper A upper D upper C upper B is not congruent to upper E upper H upper G upper F because parallelogram upper A upper D upper C upper B was dilated. Skip to navigation

Answer 1

To determine whether the two parallelograms ADCB and EHGF are congruent, we need to assess their properties and transformations.

1. **Coordinates of Points**:
- For parallelogram ADCB, we have points A (-6, 1), B (-3, 1), C (-2, 3), and D (-5, 3).
- For parallelogram EHGF, we have points E (2, 3), F (5, 3), G (6, 5), and H (3, 5).

2. **Congruence Criteria**:
- Two polygons are congruent if they have the same shape and size. This can be tested by checking if one can be transformed into the other through translations, rotations, or reflections, and they maintain their side lengths and angles.

3. **Checking Sides**:
- Calculate the lengths of the sides for both parallelograms.

For ADCB:
- AB = Distance between A and B = √[(-3 - (-6))² + (1 - 1)²] = √[3²] = 3
- BC = Distance between B and C = √[(-2 - (-3))² + (3 - 1)²] = √[1² + 2²] = √5
- CD = Distance between C and D = √[(-5 - (-2))² + (3 - 3)²] = √[3²] = 3
- DA = Distance between D and A = √[(-6 - (-5))² + (1 - 3)²] = √[1² + (-2)²] = √5

For EHGF:
- EF = Distance between E and F = √[(5 - 2)² + (3 - 3)²] = √[3²] = 3
- FG = Distance between F and G = √[(6 - 5)² + (5 - 3)²] = √[1² + 2²] = √5
- HG = Distance between G and H = √[(3 - 6)² + (5 - 5)²] = √[3²] = 3
- HE = Distance between H and E = √[(2 - 3)² + (3 - 5)²] = √[1² + (-2)²] = √5

4. **Conclusion**:
- Both parallelograms ADCB and EHGF have sides of lengths 3, √5, 3, and √5, respectively.
- Thus, the two parallelograms have the same side lengths.

5. **Transformation**:
- Since both can be shown to be the same size and shape, we can state that ADCB and EHGF are congruent. The statements about rotation, reflection, or translation can all be valid, but the most straightforward conclusion based on the problem is that they are congruent because of these properties.

Based on the reasoning given above, the correct answer is:

**Yes, ADCB≅EHGF because parallelogram ADCB was translated.**

This option confirms the congruence of the two parallelograms through the basic properties of congruence, without assuming any specific transformation scenario that may not be explicitly required to prove congruence.