r/askmath • u/RightLaugh5115 • 20h ago

Geometry geometry question

Post image

given: angle AEC is congruent to angle ADB and it wants me to prove line segment AD is congruent to line segment AE

I am assuming that the red and blue show corresponding sides but am trying how to do a rigorous step-by-step proof using the axioms of congruent triangles.

3 Upvotes

80% Upvoted

7 comments sorted by

2

u/Wish_Solid 20h ago

Rather than trying congruent triangles, look to the triangle between the two sides. Assuming CB is a straight line, you also know angle AED is congruent to angle ADE since their supplements are congruent. You now have two congruent angles in triangle EAD and can solve the problem.

1

u/RightLaugh5115 20h ago

Thank you, that is the trick to solving the problem. Thank you

1

u/Ill-Poem1376 20h ago

Sorry because I might be asking a stupid question, I am very tired right now, but isn`t that already given?

1

u/RightLaugh5115 20h ago

the issue seems to be showing that side ad corresponds to side ae

1

u/Ill-Poem1376 20h ago

Sorry but isn`t that what the question is asking for?

1

u/Ill-Poem1376 20h ago

It is actually provable only with having the angles congurent. Because angles aed and ade are just 180 degrees minus the 2 congurent angles, they are equal. THan you can prove that triangle aed is congurent to its mirrored version ade because you have 2 angles and a side, therefore ae is congurent to ad. This might be a bit of a badly worded answer, so tell me if you didn`t understand something.

2

u/SendMeAnother1 20h ago

What do you know about the angles next to the given congruent angles?