Answer:
A. AA Similarity Theorem . True
B. Two sides divided proportionally.
True
C. A parallel line to one side of a triangle. True
D. A perpendicular line to one side of a triangle. False
Step-by-step explanation:
The Triangle Proportionality Theorem says that if a line is parallel to one side of a triangle, then it splits the other two sides into proportional sections.
Now, here the given statements are:
<u>A. AA Similarity Theorem
</u>
TRUE, as the angles opposite to equal sides are equal.
And if lines are divided proportionally, both the triangles are Similar by AA similarity theorem.
<u>B. Two sides divided proportionally.
</u>
TRUE,as the other two sides of the triangle are divided proportionally by the parallel line.
<u>C. A parallel line to one side of a triangle.
</u>
TRUE, as the parallel line divides the other two non- parallel sides in equal proportions.
<u>D. A perpendicular line to one side of a triangle.</u>
FALSE, this part is not required anywhere in the given theorem result.
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![x^\frac{5}{6}=\sqrt[6]{x^5}](https://tex.z-dn.net/?f=x%5E%5Cfrac%7B5%7D%7B6%7D%3D%5Csqrt%5B6%5D%7Bx%5E5%7D)
![4x^\frac{5}{6}=4\sqrt[6]{x^5}](https://tex.z-dn.net/?f=4x%5E%5Cfrac%7B5%7D%7B6%7D%3D4%5Csqrt%5B6%5D%7Bx%5E5%7D)