Problem preview
G-CO.11 Warmup M2-035-A08-V01

Prove parallelogram theorems and their converses, including diagonal and rectangle results.

Test the opposite-sides converse for a parallelogram

Problem

Decide whether the stated side evidence is sufficient to prove a parallelogram: quadrilateral \(ABCD\) with \(AB=CD\) and \(BC=AD\).

Big Picture

What this problem is really about

This is a converse test, so every part of the theorem’s hypothesis must be established before classifying the quadrilateral. We’ll list the boundary sides in order, verify two distinct opposite congruence pairs rather than one pair or adjacent matches, and then apply the converse exactly once.

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Four variants of this problem type
Curriculum context
Course
Math II
Standard
G-CO.11
Category
Geometry
Domain
Congruence
Objective
Prove parallelogram theorems and their converses, including diagonal and rectangle results.
Problem type
Test the opposite-sides converse for a parallelogram