Question

In this diagram WQ = AC. One way to prove this is true is to draw a line through B such that BDAC. Then prove triangle ABC is congruent to triangle DCB, and use corresponding parts of the two triangles. Explain why triangle ABC is congruent to triangle DCB.
Someone help Please!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

 

We can see that line BD and line AC are two parallel lines which also intersects with other two parallel lines, line BA and line DC. Since the two sets of parallel lines intersect, then the length of BD = AC and BA = DC. And by virtue of parallel lines intersecting, then angle BAC and angle BDC are called corresponding angles. Corresponding angles are angles which have equal measurement.  To summarize the similarities:

BA = DC                                                 (Equal sides)

BD = AC                                                 (Equal sides)

angle BAC = angle BDC                     (Equal included angle)

Therefore by using the Side – Angle – Side Postulate, we can say that triangle ABC and triangle DCB are congruent triangles.

Answer 2

Answer:Therefore WQ = (1/2)AC .

Step-by-step explanation:

I think , it must be " draw a line through B such that BD is congruent and parallel to AC " .

If so then a quadrilateral ABDC becomes a parallelogram , you can prove △ABC is congruent to △DCB .

But to prove WQ = (1/2)AC , similarlity of two triangles is useful .

W is a midpoint of AB , so BW = (1/2)BA .

Q is a midpoint of BC , so BQ = (1/2)BC .

Clearly ∠WBQ = ∠ABC .

So △WBQ is similar to △ABC and the ratio of their corresponding sides is (1/2) : 1 .

Therefore WQ = (1/2)AC .