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Geometry/Trig 2 Name: __________________________

Geometry/Trig 2 Name: __________________________ Properties of Parallelograms Exploration Date: ___________________________ Please follow all directions as carefully and accurately as possible. 1. Fold your paper in half, length-wise (hotdog). Crease the fold well.

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Geometry/Trig 2 Name: __________________________

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  1. Geometry/Trig 2 Name: __________________________ Properties of Parallelograms Exploration Date: ___________________________ Please follow all directions as carefully and accurately as possible. 1. Fold your paper in half, length-wise (hotdog). Crease the fold well. 2. Use a ruler as a straight edge to draw a scalene, obtuse triangle in the top half of your paper. Make the obtuse angle between 110 and 130. 3. Carefully cut out your triangle (with the paper folded). Because the paper is folded, you should obtain two congruent triangles. It is important to keep the paper folded together as closely as possible, so that your pair of triangles stay congruent. **4. Color the three pairs of corresponding sides of the triangles three different colors. Then color each pair of corresponding angles of the triangles in the color of the opposite side. (See my example or ask questions if you are confused.) 5. Draw the median from the vertex of the obtuse angle to the longest side in each triangle using your fourth color. 6. Place the two triangles together so that the longest sides match up. **7. Label the vertices of the quadrilateral A, B, C, D, and the midpoint of the longest side of the triangle as M using a pencil. (See my example or ask questions if you are confused.) Materials: 4 different colored pencils, scissors, pencil, ruler, protractor, paper A B M D C • Examine mÐBAC and mÐACD. What is the relationship between these angles? Meaning, what type of angles are they? ________________________________________________________________________ • What can you conclude about AB and DC? _________________________________________________ • What postulate/theorem allows you to claim that? ___________________________________________ • _________________________________________________________________________________ • 2. Examine mÐACB and mÐDAC. What is the relationship between these angles? Meaning, what type of angles are they? _________________________________________________________________________ • What can you conclude about AD and BC? _________________________________________________ • What postulate/theorem allows you to claim that? ___________________________________________

  2. Geometry/Trig 2 Properties of Parallelograms Exploration 3. Look at AB and DC. What can you conclude about the two segment lengths? ________________________ 4. Look at AD and BC. What can you conclude about the two segment lengths? ________________________ 5. Based on your conclusions in numbers 3 and 4, complete the statements: AB ___ DC and AD___ BC 6. BM is a median of DABC. Draw a conclusion based on the definition of a median. _____________________ 7. DM is a median of DADC. Draw a conclusion based on the definition of a median. _____________________ 8. Based on your conclusions in numbers 6 and 7, complete the statement: AC and BD ____________________ each other. SUMMARY – Check for Understanding Quadrilateral ABCD is called a parallelogram. On the previous page you explored many of the properties of a parallelogram. Based on your findings, see if you can complete each statement to discover several properties of parallelograms. 1. The opposite sides of a parallelogram are ____________________________________. 2. The opposite sides of a parallelogram are ____________________________________. 3. The opposite angles of a parallelogram are ___________________________________. 4. The diagonals of a parallelogram ______________________________ each other.

  3. Section 5-1 Properties of Parallelograms Notes Definition of a Parallelogram: _______________________________________________ ______________________________________________________________________ Theorem 5-1: ___________________________________________________________ Proof of Theorem 5-1: Diagram: Given: _______________________ Prove: _______________________ Statements Reasons Theorem 5-2: ___________________________________________________________ H G Proof of Theorem 5-2: Given: _______________________ Prove: _______________________ 4 1 2 3 Statements Reasons E F

  4. Section 5-1 Properties of Parallelograms Notes How can we prove the other opposite angles are congruent using the information from the previous proof? Given: _______________________ Prove: _______________________ Statements Reasons H G E F Theorem 5-3: ___________________________________________________________ Q R Proof of Theorem 5-3: Given: _____________________________ Prove: _______________________ 1 3 M 4 2 T S Statements Reasons

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