Answer:
Option A
Option D
Option E
Step-by-step explanation:
we know that
If the height and base of triangle B are proportional to the height and base of triangle A
then
Triangle A and Triangle B are similar
Remember that
If two triangles are similar then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
so
where
h_A and h_B are the height of triangle A and triangle B
b_A and b_B are the base of triangle A and triangle B
In his problem we have
substitute
Rewrite
<u><em>Verify all the options</em></u>
A) we have
Find the ratio of the height to the base of triangle B and compare the result with the ratio of height to the base of triangle A (the value is 1.5625)
substitute the values in the proportion
The ratios are the same
That means that are proportional
therefore
These values could be the height and base of triangle B
B) we have
Find the ratio of the height to the base of triangle B and compare the result with the ratio of height to the base of triangle A (the value is 1.5625)
substitute the values in the proportion
The ratios are not equal
That means that are not proportional
therefore
These values could not be the height and base of triangle B
C) we have
Find the ratio of the height to the base of triangle B and compare the result with the ratio of height to the base of triangle A (the value is 1.5625)
substitute the values in the proportion
The ratios are not the same
That means that are not proportional
therefore
These values could not be the height and base of triangle B
D) we have
Find the ratio of the height to the base of triangle B and compare the result with the ratio of height to the base of triangle A (the value is 1.5625)
substitute the values in the proportion
The ratios are the same
That means that are proportional
therefore
These values could be the height and base of triangle B
E) we have
Find the ratio of the height to the base of triangle B and compare the result with the ratio of height to the base of triangle A (the value is 1.5625)
substitute the values in the proportion
The ratios are the same
That means that are proportional
therefore
These values could be the height and base of triangle B
