Question
In the drawing below, Side B A is parallel to Side D E. Triangle ABC is similar to triangle DEC.
2 triangles. Sides A B and E D are parallel. Lines B E and A D intersect at point C.
Which statement about the sides is true?
Side A B corresponds to Side C D.
Side C E corresponds to Side C A.
Side C E corresponds to Side C D.
Side B A corresponds to Side E D.
2 triangles. Sides A B and E D are parallel. Lines B E and A D intersect at point C.
Which statement about the sides is true?
Side A B corresponds to Side C D.
Side C E corresponds to Side C A.
Side C E corresponds to Side C D.
Side B A corresponds to Side E D.
Answers
Answered by
GPT-4o mini
In similar triangles, corresponding sides are in proportion and correspond to each other based on their relative positions.
Given that triangle ABC is similar to triangle DEC, we can analyze the sides:
- Since side BA is parallel to side DE, it means that triangle ABC and triangle DEC share some proportionality based on their angles.
So let’s consider the statements provided:
1. **Side AB corresponds to Side CD.** - This is incorrect because AB and CD are not corresponding sides in the given triangles.
2. **Side CE corresponds to Side CA.** - This is also incorrect. CE is part of triangle DEC, while CA is part of triangle ABC, and they are not corresponding sides.
3. **Side CE corresponds to Side CD.** - This is incorrect. CE is part of triangle DEC and does not correspond to CD.
4. **Side BA corresponds to Side ED.** - This statement is correct. Since triangles ABC and DEC are similar, side BA in triangle ABC corresponds to side DE in triangle DEC.
Therefore, the true statement about the sides is:
**Side B A corresponds to Side E D.**
Given that triangle ABC is similar to triangle DEC, we can analyze the sides:
- Since side BA is parallel to side DE, it means that triangle ABC and triangle DEC share some proportionality based on their angles.
So let’s consider the statements provided:
1. **Side AB corresponds to Side CD.** - This is incorrect because AB and CD are not corresponding sides in the given triangles.
2. **Side CE corresponds to Side CA.** - This is also incorrect. CE is part of triangle DEC, while CA is part of triangle ABC, and they are not corresponding sides.
3. **Side CE corresponds to Side CD.** - This is incorrect. CE is part of triangle DEC and does not correspond to CD.
4. **Side BA corresponds to Side ED.** - This statement is correct. Since triangles ABC and DEC are similar, side BA in triangle ABC corresponds to side DE in triangle DEC.
Therefore, the true statement about the sides is:
**Side B A corresponds to Side E D.**