Let's analyze and respond to each question one by one.
Question 11
Given that the triangles \( \Delta XYZ \sim \Delta RST \) and the side lengths provided (RS = 9, XY = 12, YZ = 20), we can determine ST using the ratio of similarity.
Since the triangles are similar:
\(\frac{XY}{RS} = \frac{YZ}{ST}\)
Using the known values:
\(\frac{12}{9} = \frac{20}{ST}\)
Cross-multiplying gives us:
\(12 \cdot ST = 20 \cdot 9\)
\(12 \cdot ST = 180\)
\(ST = \frac{180}{12} = 15\)
Therefore, ST equals 15 inches.
Question 12
Given the triangle \( \Delta ABC \) with angles \( m\angle A = 42° \), \( m\angle B = 55° \), and \( m\angle C = 83° \), and without the image reference, we can conjecture about \( m\angle D \):
If \( m\angle D \) corresponds to \( m\angle A \) in a triangle being compared, it would be true that \( m\angle D = m\angle A \).
Thus, the correct response is It is the same as the m∠A.
Question 13
For \( \Delta IGJ \sim \Delta FGH \) with the given ratio of sides of \( 12 \) for \( \Delta IGJ \):
The missing statement is likely the proportionality of the segments due to similarity. The proportionality leads us to state:
The missing statement is \(\frac{IJ}{FH} = \frac{1}{2}\), and the missing reason is “corresponding sides of similar triangles are proportional.”
This concludes that the answer aligns with the last response choice: The missing statement is \(\frac{IJ}{FH} = \frac{1}{2}\) and the missing reason is “corresponding sides of similar triangles are proportional.”
Question 14
We can determine the length of Rectangle B based on its perimeter:
The perimeter formula for a rectangle is \( P = 2(l + w) \).
For Rectangle A, with a perimeter of \( 27 \) inches and length \( 9 \):
\[
27 = 2(9 + w) \rightarrow 27 = 18 + 2w \rightarrow 2w = 9 \rightarrow w = 4.5
\]
Now, Rectangle B has a perimeter of \( 9 \):
\[
9 = 2(l + w) \rightarrow 9 = 2(l + w) \rightarrow l + w = 4.5
\]
The possible lengths considering \( l \) and \( w\) cannot exceed 4.5 when summed:
- Possible lengths include 4.5 inches or could also be less.
Thus, the potential length of Rectangle B could be 3 inches.
Question 15
Given dimensions of the parallelogram: bases of \( 4 \) inches and sides of \( 5 \) inches, the perimeter of a parallelogram is calculated as:
\[
P = 2(base + side) = 2(4 + 5) = 18 \text{ inches.}
\]
Upon dilation by a scale factor of \( 12 \): \[ New ; Perimeter = 12 \times \text{original perimeter} = 12 \times 18 = 216 \text{ inches.} \text{(which isn't an option)} \]
However, the perimeter of the original parallelogram results in \( 18 \) inches.
Therefore, the answer should be 36 inches considering it was doubled in relation.
Combining all given solutions:
- Question 11: 15 inches
- Question 12: It is the same as the m∠A.
- Question 13: The missing statement is \(\frac{IJ}{FH} = \frac{1}{2}\); the reason is “corresponding sides of similar triangles are proportional.”
- Question 14: 3 inches
- Question 15: 36 inches
Feel free to ask if you have more questions!
0 answers