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Name___________________ Proving Triangles Congruence Investigation WS Directions: Prove if the following methods are shortcut to proving triangles are congruent sometimes, always, or never. *Remember 2 ∆ `s are congruent if only if all corresponding parts are equal in measure. Using Sketchpad Find away to disprove that 2 ∆ `s are not congruent if all congruent if the following is true. Use sketch (Oneside.gsp) 1) Is ∆ XYZ ≅ ∆ ACB sometimes always never Sketch (2angles.gsp) 4) Is ∆ XYZ ≅ ∆ ACB sometimes always never Sketch (Oneangle.gsp) 2) Is ∆ XYZ ≅ ∆ ACB Sketch (2sides.gsp) 3) Is ∆ XYZ ≅ ∆ ACB sometimes sometimes always never always never Sketch (Ang-side.gsp) 5) Is ∆ XYZ ≅ ∆ ACB Sketch (3sides.gsp) 6) Is ∆ XYZ ≅ ∆ ACB sometimes sometimes always never always never Sketch (SAS.gsp) 7) 2 sides and an angle between the 2 sides are equal is ∆ XYZ ≅ ∆ ACB Sketch (SSA.gsp) 8) If 2 sides and an angle between the 2 sides are equal is ∆ XYZ ≅ ∆ ACB Sketch (ASA.gsp) 9) If 2 angles and a side between the 2 angles are equal is ∆ XYZ ≅ ∆ ACB sometimes sometimes sometimes always never Sketch (AAS.gsp) 10) If 2 angles and a side not between the 2 angles are equal is ∆ XYZ ≅ ∆ ACB sometimes always never always never always never Sketch (3angles.gsp) 11) If 3 angles are equal is ∆ XYZ ≅ ∆ ACB sometimes always never 12) Which of the following are shortcuts in the above examples in proving ∆ `s are ALWAYS congruent if this information is given in two triangles? Use the shortcuts in the following problems to identify if they are congruent. 13) Sec. 5.4 1-15 all *Draw or trace ∆ `s for each problem and explain what triangles are congruent and why. 14) Use the SSS shortcut to construct a triangle congruent to ∆ ABC. B A C 15) Use the SAS shortcut to construct a triangle congruent to ∆ RST. Use R S , ST , ∠ S. R S T 16) Construct two triangles that are not congruent but 2 sides and an angle not between them in one triangle is congruent to two sides and an angle not between them in the other triangle. 17) Sec 5.5 1-15 ALL Show all work and diagrams.
