In this diagram WQ = 1/2 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. https://dw6y82u65ww8h.cloudfront.net/organisations/328/85ffafd1-1622-41c0-936d-1da2a2b4ffb0/img_geou04l11_12.gif

Question

In this diagram WQ = 1/2  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.  https://dw6y82u65ww8h.cloudfront.net/organisations/328/85ffafd1-1622-41c0-936d-1da2a2b4ffb0/img_geou04l11_12.gif

swinn · Answer

@nicole122603 do you think you could help me with this

nicole122603 · Answer

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.

swinn · Answer

thank you