Find the unknown angle in triangles and quadrilaterals

Learning Objectives Define and identify corresponding parts of congruent triangles (CPCTC). Apply congruence postulates (SSS, SAS, ASA, AAS, HL) to prove triangles are congruent. Use the property that corresponding angles of congruent triangles are equal to find unknown angle measures. Decompose quadrilaterals into triangles to find unknown angles using congruence. Set up and solve algebraic equations for angle measures based on congruent triangle properties. Justify each step in a logical argument to find an unknown angle. Ever wonder how architects ensure a bridge's triangular supports are perfectly identical and stable? 🌉 It all comes down to the power of congruent triangles! This tutorial will show you how to use the concept of congruent triangles as a powerful to...

TermDefinitionExample Congruent TrianglesTriangles that have the exact same size and shape. All pairs of corresponding sides and corresponding angles are equal in measure.If ΔABC ≅ ΔDEF, it means AB = DE, BC = EF, AC = DF, m∠A = m∠D, m∠B = m∠E, and m∠C = m∠F. Corresponding PartsThe matching sides and angles in two congruent figures. The order of the vertices in a congruence statement tells you which parts correspond.In the statement ΔPQR ≅ ΔXYZ, ∠P corresponds to ∠X, and side QR corresponds to side YZ. CPCTCAn acronym for 'Corresponding Parts of Congruent Triangles are Congruent'. It is the reason we use to state that corresponding angles or sides are equal *after* we have proven two triangles are congruent.Once we prove ΔGHI ≅ ΔJKL by SAS, we can then conclude that ∠H ≅ ∠K beca...

CPCTC (Corresponding Parts of Congruent Triangles are Congruent) If ΔABC ≅ ΔDEF, then m∠A = m∠D, m∠B = m∠E, and m∠C = m∠F. This is the fundamental reason used *after* proving triangles are congruent. It allows you to transfer the known measure of an angle from one triangle to its corresponding angle in the congruent triangle. Triangle Angle Sum Theorem For any ΔABC, m∠A + m∠B + m∠C = 180° Use this rule to find the third angle in a single triangle once two angles are known. This is often a final step after using CPCTC to find one of the angles. Quadrilateral Angle Sum Theorem For any quadrilateral WXYZ, m∠W + m∠X + m∠Y + m∠Z = 360° Use this to find a missing angle in a quadrilateral. You may first need to use congruent triangles (formed by a diagonal) to determine the...