Problem preview
G-CO.11 Warmup M2-035-A01-V01

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

Use the opposite-sides theorem in a parallelogram to find a missing side measure or solve for a variable

Problem

In parallelogram \(ABCD\), \(AB=12\). Find the missing side measure.

Big Picture

What this problem is really about

A parallelogram transfers a side length across the figure only to the side directly opposite it. We’ll trace the boundary order, identify the pair that shares no endpoint, write their congruence before using the given measure, and check that no adjacent side was substituted.

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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
Use the opposite-sides theorem in a parallelogram to find a missing side measure or solve for a variable