Thank you for visiting Given that tex frac AE ED frac BE EC tex which of the following justifies that triangle AEB is congruent to triangle DEC A Angle. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Final answer:
Triangles AEB and DEC are congruent because angle AEB is congruent to angle DEC due to being vertical angles, as stated in option (A).
Explanation:
The student's question pertains to determining why triangles AEB and DEC are congruent given the ratio AE/ED = BE/EC. Among the choices provided, the correct justification involves understanding that angle AEB is congruent to angle DEC due to them being vertical angles, which are always congruent. The given ratios imply proportional segments but do not directly establish congruency of sides. As such, the correct choice is (A) Angle AEB is congruent to angle DEC (Vertical angles).
The statement "AE/ED = BE/EC" indicates that the triangles AEB and DEC are similar by the Side-Angle-Side (SAS) similarity criterion. This is because the ratios of corresponding sides are equal.
Now, to justify that triangle AEB is congruent to triangle DEC, you need to establish more than just similarity. You need to show that corresponding angles are congruent.
From the given information, the correct choice is:
A) Angle AEB is congruent to angle DEC (Vertical angles)
This is because vertical angles are congruent, and if AEB and DEC are similar triangles, the corresponding angles are congruent, including the vertical angles.
Thank you for reading the article Given that tex frac AE ED frac BE EC tex which of the following justifies that triangle AEB is congruent to triangle DEC A Angle. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
- You are operating a recreational vessel less than 39 4 feet long on federally controlled waters Which of the following is a legal sound device
- Which step should a food worker complete to prevent cross contact when preparing and serving an allergen free meal A Clean and sanitize all surfaces
- For one month Siera calculated her hometown s average high temperature in degrees Fahrenheit She wants to convert that temperature from degrees Fahrenheit to degrees
Rewritten by : Jeany
