Altitudes in Right Triangles Quick Check 1 of 51 of 5 Items Question Use the image to answer the question. Given is the right triangle ABC with altitude CO . Which one of the following statements is true and contributes to the proof of the Pythagorean Theorem? (1 point) Responses △ABC∼△AOC triangle upper A upper B upper C congruent to triangle upper A upper C upper O △AOC∼△COB triangle upper A upper B upper C congruent to triangle upper A upper C upper O △AOC∼△BOC triangle upper A upper B upper C congruent to triangle upper A upper C upper O △ABC∼△BOC triangle upper A upper B upper C congruent to triangle upper A upper C upper O Skip to navigation page 15 of 15 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

Answer 1

To assess which statement contributes to the proof of the Pythagorean Theorem using the right triangle ABC with altitude CO, we should consider the relationships between the triangles formed by the altitude.

In triangle ABC:

• The area of triangle ABC can be expressed in two ways: using the base and height, and using the two right triangles formed by the altitude.
• When you drop the altitude CO from vertex C to side AB, it results in two smaller right triangles: AOC and BOC.

Using the property of similar triangles, we find that:

1. Triangle AOC is similar to triangle ABC.
2. Triangle BOC is similar to triangle ABC.
3. Triangle AOC is similar to triangle BOC.

The important relationships here are based on the similarities, which give us proportional relationships that can be used to derive the Pythagorean Theorem.

Among the options given, the most relevant statement to the proof of the Pythagorean Theorem would typically include relationships like:

• "△ABC ∼ △AOC" (Triangle ABC is similar to triangle AOC.)
• "△ABC ∼ △BOC" (Triangle ABC is similar to triangle BOC.)
• "△AOC ∼ △BOC" (Triangle AOC is similar to triangle BOC.)

However, without the specific properties indicated in the statements, a direct suggestion for the best answer would generally be one that proposes a similarity that relates all parts of triangle ABC (the large triangle) to one of the smaller triangles (either AOC or BOC), leading to the conclusion of the Pythagorean Theorem.

If I were to speculate which is often used in context, the response that shows "△ABC∼△AOC" is a common statement used in proofs related to the altitude in right triangles and contributes significantly to the proof itself.

Please confirm with the options you have, and we can refine it further based on the specific wording.