According to the AA similarity theorem, the statement that must be true is: D. ∠Z ≅ ∠W and ∠X ≅ ∠U.
<h3>What is the AA Similarity Theorem?</h3>
The AA similarity theorem states that if two angles in one triangle is congruent to two corresponding angles in another triangle, then both triangles are similar.
For △ZYX ~ △WVU, any two pairs of corresponding angles must be congruent.
Therefore, the statement that must be true based on the AA similarity theorem is: D. ∠Z ≅ ∠W and ∠X ≅ ∠U.
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Answer:
5. B, C and E
6. C
7. None
8. A and D
9. F and G
Step-by-step explanation:
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5. B, C and E
B, C and E are not parallelogram because they do not have 2 pairs of parallel sides
B and E are trapeziums while C is just a quadrilateral.
6. C
In (5) above, we established that B and E are trapeziums while C is not. This implies that only C is a quadrilateral.
7. None
A square is a parallelogram. So, it is not possible for a shape to be a square and not be a parallelogram.
8. A and D
A is a rhombus. D is a square and will be treated as a rhombus because all sides are equal.
9. F and G
These shapes have 2 pairs of parallel lines but all 4 sides are not equal; only the opposite sides are equal.
Well we have the equation d = r * t
(d stands for distance, r for rate, and t for time)
So, plug in our values:
d = 55 *4
And, d = 220
I can't see the answer choices, but I hope this will help you!! Let me know if you have ANY questions.
The definition of similar triangles says that 2 triangles are similar if they have the same shape but different size. There are two criteria to check for this:
1) If all angles in one triangle are equal to the angles in another one, then the 2 are equal.
2) If the sides have the same proportions, then the 2 triangles are similar.
1) We have that all the angles of the 2 triangles have an equal angle in the other triangle. In specific, Q is matched to B, P to A and R to C. Hence, since corresponding angles are congruent, the two triangles are similar.
2) Here we are given information about the sides of the triangles, so we will check the second criterion. We form the ratio of the largest sides of each trangle and the shortest sides. 30/5=6. For the shortest sides, 18/3=6. Finally for the middle sides, 24/4=6. Hence, we have that the triangles are similar since the ratios are equal. (it doesn't matter whether we take the bigger or the smaller side as a numerator, as long as we are consistent).
Answer: 2+q
Step-by-step explanation:
