To analyze the dilated triangle \( \Delta A'B'C' \) produced from \( \Delta ABC \) (which is a right triangle), we need to apply the properties of dilation.
Given:
- The original triangle \( \Delta ABC \) is right-angled at \( B \) with:
- \( AB = 3 \) units,
- \( BC = 4 \) units,
- The hypotenuse \( AC = 5 \) units,
- The angles are \( m\angle A = 37^\circ \), \( m\angle B = 90^\circ \), and \( m\angle C = 53^\circ \).
When a figure is dilated by a factor of \( k \), each side length is multiplied by \( k \), and the angles remain unchanged.
Since the triangle is dilated by a factor of \( 2 \):
- The new side lengths will be:
- \( A'B' = 2 \times AB = 2 \times 3 = 6 \) units
- \( B'C' = 2 \times BC = 2 \times 4 = 8 \) units
- \( A'C' = 2 \times AC = 2 \times 5 = 10 \) units
The angles remain the same:
- \( m\angle A' = m\angle A = 37^\circ \)
- \( m\angle B' = m\angle B = 90^\circ \)
- \( m\angle C' = m\angle C = 53^\circ \)
Now let's evaluate the statements:
A. B'C' = 6 units
This statement is not true because \( B'C' = 8 \) units, not 6.
B. m∠C' = 53°
This statement is true as angles remain the same under dilation.
C. A'C' = 10 units
This statement is also true because \( A'C' \) is \( 10 \) units.
D. m∠A' = 74°
This statement is not true since \( m\angle A' = 37^\circ \).
The incorrect statements are A and D. However, since A is specifically focused on the calculated length and D is about angle measurement (which should not change), the best pick here is that statement A is definitely incorrect.
So, the answer is: A. B'C' = 6 units is not true.