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.

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.)

How to do so? I'm confused. Help is appreciated, thanks.

asked by Sam
  1. if Theta is 90 deg, you have to conclude that all sides are congruent.

    posted by bobpursley

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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.
  2. 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.
  3. 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.
  4. Math please help!!

    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.
  5. Math

    1. If Angle ABC is congruent to Angle DEF by side-side-side triangle congruence, the angle B is congruent to Angle E by? A) Side-angle-side congruence. B) Angle-angle-side congruence. C) Corresponding parts of congruence. D)
  6. geomerty

    The following triangles, Ä ABC and Ä DEF, are congruent. abc 67.38degree 12cm lenght 22.62degree b5cm,l,13cm Find the lengths of all missing sides and measures of all angles for both triangles. Include correct units with each of
  7. Math Geometry

    Geometry Question: Prove the symmetric Property for congruence of triangles. Given: ∆ABC≅ ∆DEF Prove: ∆DEF≅ ∆ABC
  8. geometry

    Suppose right triangle ABC has one acute angle 47º. Suppose also that right triangle DEF has an acute angle 43º. How are triangles ABC and DEF related?
  9. Geometry.

    Triangles ABC and DEF are similar. If ∠ABC = 121°and ∠BCA = 35°, find the measure of angle FDE.
  10. geometry

    DEF and ABC are complementary angles and ABC is nine times as large as DEF. Determine the measure of each angle.

More Similar Questions