Problem preview
G-CO.8 Warmup M1-043-A07-V01

Explain ASA, SAS, and SSS triangle congruence criteria from rigid-motion congruence.

Use the reflexive property for a shared triangle part

Problem

Apply the reflexive property to side \(AC\), shared by triangles \(ABC\) and \(ADC\). State the congruence relationship and explain why it applies.

Big Picture

What this problem is really about

The reflexive property is about identity, so first trace the boundary that both triangles literally use. A segment that appears in only one triangle cannot supply the shared fact; the same physical segment appearing in both can be written as congruent to itself and used alongside the other givens.

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Four variants of this problem type
Curriculum context
Course
Math I
Standard
G-CO.8
Category
Geometry
Domain
Congruence
Objective
Explain ASA, SAS, and SSS triangle congruence criteria from rigid-motion congruence.
Problem type
Use the reflexive property for a shared triangle part