Mathematics, 09.05.2021 22:20 nettaboo4664
In the figure, AB is parallel to CD, XY is the perpendicular bisector of AB, and E is the midpoint of XY. Prove that △AEB ≅ △DEC by matching each mathematical statement with its reason.
*(select) = A, B, C, D, E, F, G, H, I, J
A. XY is perpendicular to AB. (select) Definition of a perpendicular bisector
B. XY ⊥ CD (select) ASA Triangle Congruence
C. m∠AXE = 90°, m∠DYE = 90°. (select) Definition of a midpoint
D. ∠AXE ≅ ∠DYE. (select) In a plane, if a transversal is
perpendicular to one of two parallel
lines, then it is perpendicular to the other.
E. XE ≅ YE (select) Vertical Angles Theorem
F. ∠A ≅ ∠D (select) Definition of perpendicular lines
G. △AEX ≅ △DEY (select) Right angles are congruent.
H. AE ≅ DE (select) AAS Triangle Congruence
I. ∠AEB ≅ ∠DEC (select) Alternate Interior Angles Theorem
J. △AEB ≅ △DEC (select) Corresponding parts of congruent
triangles are congruent.
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