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Congruence

A question in my revision I have just come across has befuddled me..

The question is:
ABC is an equilateral triangle (A at top, B left, C right)
D lies on BC (Line through center of angle, locus to both sides)
AD is perpendicular to BC
Prove that triangle ADC is congruent to triangle ABD
(btw brackets were not on the paper)

The reason for this confusion is because after answering the question I got RHS (right angle, hypotenuse, side) this is because the triangle is equilateral and so the two hypotenuses of the new triangles are congruent (so that ticks of hypotenuse), they both have right angles from the point that D cuts through BC perpendicular to it (so at a right angle, checking that of the list) and finally they both have the same side AD. This draw me to the conclusion that they are congruent because of RHS but the answer in the booklet gives ASA, now am I wrong, are we both right? If I were to write this down in the exam will I get no marks?

Reply 1

Knee Grow

Both of those answers sound perfectly correct to me. I personally would have used your method.

Posted from TSR Mobile

(edited 9 years ago)

Reply 2

Smaug123

Original post by BrainJuice

This draw me to the conclusion that they are congruent because of RHS but the answer in the booklet gives ASA, now am I wrong, are we both right?

Any of these do indeed work. My preferred way of doing it would be to note that "look, if you fold the diagram along the line AD, you get a single right-angled triangle - indeed, what else could you possibly get? If you got a different shape depending on whether you folded it leftways or rightways, that would just be ridiculous, because of symmetry - performing the same experiment with the original equilateral triangle flipped changes nothing. Hence the resulting shapes are congruent.". That, of course, might not get the marks, but it works for any vertically symmetrical shape, not just triangles.

Your RHS answer is absolutely fine, though.