To determine which statement is not true, we need to understand the properties of dilation. When a triangle is dilated by a factor, the angles remain the same, but the side lengths are scaled by the dilation factor.

Given that ΔABC is dilated by a factor of 2 to produce ΔA'B'C', let's analyze each statement:

A. $ m∠B' = 62° $
- Since dilation does not change the angles, $ m∠B' $ should be equal to $ m∠B $. Therefore, if $ m∠B = 62° $, then $ m∠B' = 62° $ is true.

B. $ A'B' = 60 $ units
- If $ A'B' $ is 60 units, then the original side $ AB $ should be $ \frac{60}{2} = 30 $ units. This statement could be true if $ AB $ was originally 30 units.

C. $ B'C' = 32 $ units
- If $ B'C' $ is 32 units, then the original side $ BC $ should be $ \frac{32}{2} = 16 $ units. This statement could be true if $ BC $ was originally 16 units.

D. $ m∠A' = 28° $
- Since dilation does not change the angles, $ m∠A' $ should be equal to $ m∠A $. Therefore, if $ m∠A = 28° $, then $ m∠A' = 28° $ is true.

To find the statement that is not true, we need to check the consistency of the angles. Since dilation does not change the angles, the sum of the angles in ΔABC and ΔA'B'C' must be 180°.

If $ m∠B = 62° $ and $ m∠A = 28° $, then:
$$ m∠C = 180° - (m∠A + m∠B) = 180° - (28° + 62°) = 90° $$

So, the angles in ΔABC are 28°, 62°, and 90°. After dilation, the angles in ΔA'B'C' should remain the same: 28°, 62°, and 90°.

Given this, all the angle statements (A and D) are consistent with the properties of dilation. Therefore, the side length statements (B and C) need to be checked for consistency with the given information.

Since the angles are consistent, the side lengths should also be consistent with the dilation factor. Both B and C could be true if the original side lengths were 30 units and 16 units, respectively.

Thus, all statements A, B, C, and D appear to be true based on the given information. However, since the question asks for the statement that is not true, we need to identify any inconsistency.

Upon closer inspection, there is no inconsistency in the given statements based on the properties of dilation. Therefore, it seems there might be an error in the question itself, as all statements provided are consistent with the properties of dilation.

If we must choose one, we would need additional information to definitively identify an inconsistency. However, based on the given information, all statements appear to be true.

Question

To determine which statement is not true, we need to understand the properties of dilation. When a triangle is dilated by a factor, the angles remain the same, but the side lengths are scaled by the dilation factor.

Given that ΔABC is dilated by a factor of 2 to produce ΔA'B'C', let's analyze each statement:

A. $ m∠B' = 62° $
- Since dilation does not change the angles, $ m∠B' $ should be equal to $ m∠B $. Therefore, if $ m∠B = 62° $, then $ m∠B' = 62° $ is true.

B. $ A'B' = 60 $ units
- If $ A'B' $ is 60 units, then the original side $ AB $ should be $ \frac{60}{2} = 30 $ units. This statement could be true if $ AB $ was originally 30 units.

C. $ B'C' = 32 $ units
- If $ B'C' $ is 32 units, then the original side $ BC $ should be $ \frac{32}{2} = 16 $ units. This statement could be true if $ BC $ was originally 16 units.

D. $ m∠A' = 28° $
- Since dilation does not change the angles, $ m∠A' $ should be equal to $ m∠A $. Therefore, if $ m∠A = 28° $, then $ m∠A' = 28° $ is true.

To find the statement that is not true, we need to check the consistency of the angles. Since dilation does not change the angles, the sum of the angles in ΔABC and ΔA'B'C' must be 180°.

If $ m∠B = 62° $ and $ m∠A = 28° $, then:
$$ m∠C = 180° - (m∠A + m∠B) = 180° - (28° + 62°) = 90° $$

So, the angles in ΔABC are 28°, 62°, and 90°. After dilation, the angles in ΔA'B'C' should remain the same: 28°, 62°, and 90°.

Given this, all the angle statements (A and D) are consistent with the properties of dilation. Therefore, the side length statements (B and C) need to be checked for consistency with the given information.

Since the angles are consistent, the side lengths should also be consistent with the dilation factor. Both B and C could be true if the original side lengths were 30 units and 16 units, respectively.

Thus, all statements A, B, C, and D appear to be true based on the given information. However, since the question asks for the statement that is not true, we need to identify any inconsistency.

Upon closer inspection, there is no inconsistency in the given statements based on the properties of dilation. Therefore, it seems there might be an error in the question itself, as all statements provided are consistent with the properties of dilation.

If we must choose one, we would need additional information to definitively identify an inconsistency. However, based on the given information, all statements appear to be true.

Knowee AI · Accepted Answer