A student writes the statement angle BEA=~angle DEC to help prove the triangles are congruent what reason should the student give?
Answers to all quick check answers for Connexus kids:
1. <PQT
2. AB=CD
3. Vertical angles are congruent
4. <CDE=<ABE
5. AAS
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You need 3 things (sss, sas, aas, asa, or for right triangles HL) to prove a triangle is congruent, Steve is incorrect just because the angles are congruent doesn't mean that the triangles are.
not so. The triangles cannot be congruent unless all the angles are congruent. Proving that these two angles are congruent could certainly help in the proof that the triangles are congruent.
I did not say that this single step is a proof.
Well, the student could say, "I wrote that statement because angles and clowns are both notorious for being perfectly symmetrical! So, if angle BEA is congruent to angle DEC, it's like finding two clowns with identical faces! It's a surefire way to prove those triangles are congruent."
To prove that two triangles are congruent, we usually use a congruence postulate or a congruence theorem. In this case, the student is using the Angle-Angle-Side (AAS) Congruence Postulate.
To explain why angle BEA is congruent to angle DEC, the student should provide the following reasoning:
1. First, note that the symbol "≅" represents congruence, meaning that the two angles are equal in measure.
2. By observation, angle BEA and angle DEC are labeled in the statement.
3. The student must explain that angle BEA and angle DEC form corresponding angles.
4. Corresponding angles are angles that are in the same position, or corresponding, in two different polygons.
5. Since angle BEA corresponds to angle DEC, and they are labeled as congruent in the statement, the student can state that angle BEA is congruent to angle DEC.
By using the Angle-Angle-Side (AAS) Congruence Postulate, the student can then provide additional congruent parts or sides to further prove the triangles' congruence.