Answered

Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

Geometry Question: Given segment EA is parallel segment DB, segment EA is congruent to segment DB, and B is the mid of segment AC; Prove: segment EB is parallel to segment DC (reference diagram in picture)

Geometry Question Given Segment EA Is Parallel Segment DB Segment EA Is Congruent To Segment DB And B Is The Mid Of Segment AC Prove Segment EB Is Parallel To S class=

Sagot :

Construction: Join ED.

The corresponding diagram is given below,

According to the given problem,

[tex]\begin{gathered} AE=BD \\ AE\parallel BD \end{gathered}[/tex]

Since a pair of opposite sides are parallel and equal, it can be claimed that quadrilateral ABDE is a parallelogram.

Then, as a property of any parallelogram, it can be argued that,

[tex]\begin{gathered} AB=DE \\ AB\parallel DE \end{gathered}[/tex]

Given that B is the mid-point of AC,

[tex]\begin{gathered} AB=BC \\ AB\parallel BC \end{gathered}[/tex]

Combining the above two results,

[tex]\begin{gathered} BC=DE \\ BC\parallel DE \end{gathered}[/tex]

It follows that ABCD also forms a parallelogram.

Again using the property that opposite sides of a parallelogram are equal and parallel. It can be claimed that,

[tex]\begin{gathered} EB=DC \\ EB\parallel DC \end{gathered}[/tex]

Hence proved that segment EB is parallel to segment DC,

[tex]\vec{EB}=\vec{DC}[/tex]

View image CaesarZ80479
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.