Prove triangles congruent

Start lessonBegins with Triangle congruence rigid motions · Slides

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HSG.CO.B.7

**HSG.CO.B.7**: Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

HSG.CO.B.7: Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

What you'll learn

State and explain the biconditional: two triangles are congruent (via rigid motions) if and only if all three pairs of corresponding sides are congruent and all three pairs of corresponding angles are congruent
Prove the forward direction: if two triangles are congruent (a rigid motion maps one to the other), then all corresponding pairs of sides and angles are congruent
Prove the reverse direction: if all corresponding pairs of sides and angles are congruent, then a sequence of rigid motions can be constructed that maps one triangle onto the other
Apply the principle of Corresponding Parts of Congruent Triangles are Congruent (CPCTC) to deduce side and angle congruences from established triangle congruence
Construct an explicit rigid-motion sequence mapping one triangle onto a congruent triangle, given corresponding vertex pairs

Review first:

Use rigid motions for congruence

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Triangle congruence rigid motions

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