# Precalculus

In most geometry courses, we learn that there's no such thing as "SSA Congruence". That is, if we have triangles ABC and DEF such that AB = DE, BC = EF, and angle A = angle D, then we cannot deduce that ABC and DEF are congruent.

However, there are a few special cases in which SSA "works". That is, suppose we have AB = DE = x, BC = EF = y, and angle A = angle D = theta. For some values of x, y, and theta, we can deduce that triangle ABC is congruent to triangle DEF. Use the Law of Cosines or Law of Sines to explain the conditions x, y, and/or theta must satisfy in order for us to be able to deduce that triangle ABC is congruent to triangle DEF. (In other words, find conditions on x, y, and theta, so that given these values, you can uniquely reconstruct triangle ABC.)

I know that one case is if theta is 90 degrees.

## Similar Questions

In most geometry courses, we learn that there's no such thing as "SSA Congruence". That is, if we have triangles ABC and DEF such that AB=DE, BC=EF, and ∠A=∠D, then we cannot deduce that ABC and DEF are congruent.
2. ### math

In most geometry courses, we learn that there's no such thing as "SSA Congruence" . That is, if we have triangles ABC and DEF such that AB = DE, BC = EF, and angle A = angle D, then we cannot deduce that ABC and DEF are congruent.
3. ### Trigonometry/Geometry

In most geometry courses, we learn that there's no such thing as "SSA Congruence". That is, if we have triangles ABC and DEF such that AB = DE, BC = EF, and angle A = angle D, then we cannot deduce that ABC and DEF are congruent.
4. ### Trigonometry/Geometry - Law of sines and cosines

In most geometry courses, we learn that there's no such thing as "SSA Congruence". That is, if we have triangles ABC and DEF such that AB = DE, BC = EF, and angle A = angle D, then we cannot deduce that ABC and DEF are congruent.
5. ### Geometry

Which of the following is not a postulate used to prove the congruence of two triangles? a. ASA b. SSA c. SAS d. SSS I think its C?
6. ### Geometry

Which answer is not a theorem or postulate used to prove triangles similarity? SAS SSA ~~my choice SSS AA
7. ### math

I'm doing The Ambiguos case of triangles given SSA. My givens are a=6; b=7; alpha=30 degrees. how do I know if there's 2 triangles?
8. ### 11th grade

I'm doing The Ambiguos case of triangles given SSA. My givens are a=6; b=7; alpha=30 degrees. how do I know if there's 2 triangles?
9. ### geometry

which triangle congruence theorem explains why all triangles are rigid? is it SSS, SAS, ASA, or AAS?
10. ### Geometry

Which of the following is NOT a way you can show that triangles are similar? ________________________________________ A. AAA similarity B. SAS similarity C. SSA similarity D. SSS similarity

More Similar Questions