what are the same measurments

Question

what is the answer

 

Answer 1

Hi Alex--

 

To see which measurements are same ("congruent"), look at the little hash marks. All the segments that have one hashmark are congruent to one another; all the ones with 2 hashmarks are congruent to one another; all the ones with 3 hashmarks are congruent to one another.

 

So for example, segments AB, BC, CD, and DE are all congruent, that is, they are the same length. 

 

Also, you may not need to do any more than that, but the cool thing is, since triangle CDE is isosceles (two congruent sides) it means their opposite angles are also congruent. Since you know the third angle there is 54, you know the other 2 have to add up to 126 (all triangles add up to 180 degrees). So each of those 2 congruent angles has to be half of 126, which means each is 63.

 

Now that you know that, you can start filling in ALL the remaining angles based on what you know about complementary and supplementary angles and that 180 rule. (You might have to extend a few of the segments so you can create more triangles...)

 

Hope this helps!

 

Matt in NY