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Yes, triangles ABC and DEF can be considered equal (congruent) if they meet specific criteria, such as having all corresponding sides and angles equal. The postulate that applies in this case is the Side-Side-Side (SSS) Congruence Postulate, which states that if three sides of one triangle are equal to three sides of another triangle, the triangles are congruent. Other applicable postulates include Side-Angle-Side (SAS) and Angle-Side-Angle (ASA), depending on the given information.
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Is ABC DEF If so name the congruence postulate that applies.?
Yes, triangles ABC and DEF are congruent if all corresponding sides and angles are equal. The congruence postulate that applies in this case could be the Side-Angle-Side (SAS) postulate, which states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent. Other applicable postulates include Side-Side-Side (SSS) and Angle-Angle-Side (AAS), depending on the known measurements.
Is ABC trangle an trangle DEF If so name which similarity postulate or theorem applies.?
None; because there is no justification for assuming that the two triangles (or trangles, as you prefer to call them) are similar.
What are congruence theorems and postulates?
If the sides AB, BC and CA of triangle ABC correspond to the sides DE, EF and FD of triangle DEF, then the two triangles are congruent if:AB = DE, BC = EF and CA = FD (SSS)AB = DE, BC = EF and angle ABC = angle DEF (SAS)AB = DE, angle ABC = angle DEF, angle BCA = angle EFD (ASA)If the triangles are right angled at A and D so that BC and EF are hypotenuses, then the triangles are congruent ifBC = EF and AB = DE (RHS)BC = EF and angle ABC = angle DEF (RHA).
Given that ABC DEF what is the measure of E?
Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. Please resubmit your question spelling out the symbols as "plus", "minus", "equals" etc. There is, therefore, no visible symbol between ABC and DEF (<, =, >, ≠ etc). Furthermore, there is no information as to whether ABC is an angle, a triangle, an arc.
What else would need to be congruent to show that abc def by aas?
Nothing else, the angle-angle-side is sufficient to show the triangles are congruent. With two corresponding angles are equal, the third angles in the triangles by definition (the sum of the three angles in a triangle is 180o) must be equal making the triangles similar. If a corresponding pair of sides are also equal, then the other two corresponding pairs of sides will be equal.
