Download Triangle Congruence Properties • Part One Side, Side, Side (SSS

Triangle Congruence Properties
Discovery Activity
big question: What pieces of information prove that two triangles are congruent? • Part One Side, Side, Side (SSS)
Given: All sides congruent
Directions:
1. Put the straws of different lengths together. 2. Form a triangle with the other set of straws. 3. Measure the angles in both triangles using a protractor. (may need to trace) 4. Respond to questions and conclusion. Questions:
1. What is the relationship between the angles of each triangle? 2. Are the triangles congruent? Why? 3. Can the straws be rearranged to form a triangle with different angles? 4. What can we conclude about triangle congruence when all sides (SSS) are congruent? • Part Two Side, Angle, Side (SAS)
Given: Two sides and the included angle congruent
Directions:
1. Place 2 of the straws on paper and form a 60°angle between them using the cut-­‐out. 2. Place 2 of the straws of the same length on the paper and also form a 60° angle between them. 3. Draw a line to represent the 3rd side. Repeat the process of the 2nd triangle. 5. Measure the length of the 3rd side and other 2 angles on both triangles. Questions:
1. What is the length of the 3rd side for each triangle? 2. Are the triangles congruent? Why? 3. What can we conclude about triangle congruence when all two sides and the included angles (SAS) are congruent? • Part Three Angle, Side, Angle (ASA)
Given: Two sides and the included angle congruent
Directions:
1. On the paper, take one straw and place two of the cut-­‐out angles at each end. 2. Repeat the process for the second triangle. 2. Using a ruler, draw a segment along each of the angles. The two angles should intersect forming the last angle. Repeat the process for the second triangle. 5. Measure the lengths of the 2 sides and the 3rd angle in both triangles. Questions:
1. What is the measure of the 3rd angle for each triangle. 2. What is the measure of the remaining 2 sides of each triangle? 3. Are the triangles congruent? Why? 4. What can we conclude about triangle congruence when two angles and the included side (ASA) are congruent? • Part Four Angle, Angle, Angle (AAA)
Given: All congruent angles
Directions:
1. Place the 3 angles so that they can form a triangle without measuring the sides initially. Draw segments connecting the angles. 2. Repeat the process for the second triangle. 3. Measure the three sides for each triangle. Questions
1. Are the triangles congruent? Why? 2. What can we conclude about triangle congruence when all angles are congruent? • Additional Relationships
Use the straws and angles to try to determine whether the following relationships would prove that two triangles are congruent. 1.) What if two triangles have one side congruent and the next two consecutive angles (SAA) are congruent? 2.) What if two triangles have a side, the next side, and the next angle (SSA) congruent? 3.) What if two right triangles have a hypotenuse, leg, and right angle (HL) congruent? (exception to #2!) • Conclusions
Place the following acronyms in the boxes depending on whether they CAN or CANNOT be used to prove triangle congruence: SSS, SAS, ASA, AAA, SAA, SSA, HL Remember: S means corresponding sides of the triangle are congruent A means corresponding angles of the triangle are congruent H and L mean corresponding legs and hypotenuses are congruent in right triangles CAN be used to prove triangle congruence CANNOT be used to prove triangle congruence Are the following pairs of triangles congruent? If so, provide the Triangle Congruence Property that supports your conclusion. 1. 2. 3. 4. • Practice
Are the following pairs of triangles congruent? If so, provide the Triangle Congruence Property that supports your conclusion. Complete the following PROOFS of triangle congruence. 10. 11. 12. Construct your own proofs for the following: