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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).
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.
How can you make a concave hexagon from four triangles?
It's a bit hard to explain in words. Suppose you have four congruent isosceles triangles: ABC, DEF, GHI, and JKL. (the vertexes are A, D, G and J). Place DEF and ABC so that the bases are touching. You now have quadrilateral ABDC ( when 2 points coincide, use the letter which comes first in the alphabet). Place GHI so that G is at B and H is at A. You now have quadrilateral AIDC (IBD is a straight line).Place JKL so that L is at D and J is at B. Now AIBKDC is the concave hexagon.
Is ABC equal to DEF if so what is the postulate that applies?
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.
