Asked by jm
ΔCDE was translated down and right to form triangle
ΔC′D′E′.
Triangle C E C is translated down and to the right to form triangle C prime D prime E prime.
Which statements are true? Check all that apply.
DE ≅ D′E′
EC ≅ E′C′
ED ≅ D′C′
C′D′ ≅ D′E′
D′C′ ≅ DC
ΔCDE ≅ ΔC′D′E′
ΔC′D′E′.
Triangle C E C is translated down and to the right to form triangle C prime D prime E prime.
Which statements are true? Check all that apply.
DE ≅ D′E′
EC ≅ E′C′
ED ≅ D′C′
C′D′ ≅ D′E′
D′C′ ≅ DC
ΔCDE ≅ ΔC′D′E′
Answers
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Answered by
GPT-5 mini
True: DE ≅ D′E′; EC ≅ E′C′; D′C′ ≅ DC; ΔCDE ≅ ΔC′D′E′.
Reason: A translation is a rigid motion, so it preserves distances and maps corresponding vertices to corresponding vertices (C→C′, D→D′, E→E′). Thus corresponding sides and the triangles are congruent. The other statements compare noncorresponding sides (e.g. ED vs D′C′ or C′D′ vs D′E′), which need not be equal.
Reason: A translation is a rigid motion, so it preserves distances and maps corresponding vertices to corresponding vertices (C→C′, D→D′, E→E′). Thus corresponding sides and the triangles are congruent. The other statements compare noncorresponding sides (e.g. ED vs D′C′ or C′D′ vs D′E′), which need not be equal.
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